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\begin{document}

\title{Disentangling Conditional Effects of Multiple Regime Shifts on Atlantic
Cod Productivity}



\author[1]{Tommi Perälä}%
\author[2]{Jeffrey Hutchings}%
\author[3]{Esben Olsen}%
\affil[1]{University of Jyvaskyla}%
\affil[2]{Dalhousie University}%
\affil[3]{Institute of Marine Research}%


\vspace{-1em}



  
  \date{May 06, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
Regime shifts are increasingly prevalent in the ecological literature.
However, definitions vary, and many detection methods are subjective.
Here, we employ an operationally objective means of identifying regime
shifts, using a Bayesian online change-point detection algorithm able to
simultaneously identify shifts in the mean and(or) variance of time
series data. We detected multiple regime shifts in long-term (59-154
years) patterns of coastal Norwegian Atlantic cod (\textgreater{}70\%
decline) and putative drivers of cod productivity: North Atlantic
Oscillation (NAO); sea-surface temperature; zooplankton abundance;
fishing mortality (F). The consequences of an environmental or
climate-related regime shift on cod productivity are accentuated when
regime shifts coincide, fishing mortality is high, and populations are
small. The analyses suggest that increasing F increasingly sensitized
cod in the mid 1970s and late 1990s to regime shifts in NAO, zooplankton
abundance, and water temperature. Our work underscores the necessity of
accounting for human-induced mortality in RS analyses of marine
ecosystems.%
\end{abstract}%



\sloppy




\textbf{Introduction}

The marine ecological and fisheries literature is increasingly replete
with references to regime shifts (M\selectlanguage{ngerman}öllmann 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,
sequential\emph{t} -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, \emph{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.

\textbf{Materials and methods}

The BOCPD algorithm (Adams and MacKay 2007) is based on sequential
Bayesian posterior estimation of the length of the current regime (run
length) and the regime-specific parameters of the underlying predictive
model (mean and variance). The recursion for calculating the posterior
distribution of the run length\(r_{t}\) at time
\(t\) given the observations\(y_{1:t}=(y_{1},...,y_{t})\) is\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(p\left(r_{t}\middle|r_{t-1}\right)=\left\{\begin{matrix}\text{\ \ \ }\frac{1}{\lambda},&amp;\mathrm{\text{if}}\text{\ \ \ }r_{t}=0\\
1-\frac{1}{\lambda},&amp;\mathrm{\text{if}}\ {\text{\ \ }r}_{t}=r_{t-1}+1\\
\ \ \ \ 0,&amp;\mathrm{\text{otherwise\ \ \ \ \ }}\mathrm{\text{\ \ \ \ \ \ }}\mathrm{\text{\ \ \ \ }}\\
\end{matrix}\text{\ \ \ }\right.\ .\) & ( 2 )\tabularnewline
\bottomrule
\end{longtable}

where \(p\left(r_{t}\middle|r_{t-1}\right)\) is the change point prior distribution
containing our prior beliefs about the probability of a regime shift. We
assume constant prior probability for a shift defined by the hazard rate
parameter \(\lambda\),

The underlying predictive model (UPM),\(p\left(y_{t}\middle|y_{t-1}^{\left(r_{t-1}\right)}\right)\), is the
predictive density conditional on the run length and thus on the latest
\(r_{t-1}\) observations, i.e.,\(y_{t-1}^{\left(r_{t-1}\right)}=y_{(t-r_{t-1}):(t-1)}\). The UPM is
used to give more weight to those run lengths that better predict the
new observation, and it is defined by the observation model,\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(p\left(y_{t}\middle|\mu,\sigma\right)=\frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{1}{2\sigma^{2}}\left(y_{t}-\mu\right)^{2}}.\) & ( 3 )\tabularnewline
\bottomrule
\end{longtable}

If none of the existing runs explains the new observation well enough,
the prior predictive density,\(p\left(y_{t}\middle|y_{t-1}^{\left(0\right)}\right)\), will dominate,
resulting in a high posterior probability for a regime shift.

As we are mostly interested in retrospective analysis of regime shifts,
we use the smoothed run length probabilities to find the most likely
segmentation of the data or the most likely set of regimes by maximizing
the product of run length probabilities over the whole time series
(Per\selectlanguage{ngerman}älä et al. 2016). We can find the maximum among all possible
combinations of regimes or we can focus on some subset of regimes by
setting certain constraints for the regimes. We have decided to set a
constraint for the minimum length of the regimes (\(M\)).
This constraint is not used for the first and the last regimes, though,
since their start and end points can be outside the time frame of our
data. We use uniform priors for the mean and variance parameters in each
of the time series analyzed. The lower and upper limits for the uniform
priors were assigned so that all plausible parameter values were
contained in the intervals. The posterior inference of the observation
model parameters is carried out by a sequential Monte Carlo algorithm
(Perälä et al. 2016), using 100,000 particles.

\emph{Model parameters}

There are two key parameters in the regime shift detection method. The
first is the minimum length of each regime, \emph{M} (\emph{M} =10 would
imply a minimum regime length of 10 year). For some data sets,
\emph{M}can be informed by prior knowledge. The suggestion has been
made, for example, that the NAO data exhibit decadal variability (e.g.,
Hurrell 1995). This might provide a defensible `default' value of
\emph{M} =10.

In general, we can see a cogent argument for maintaining \emph{M} at 10
years for all data sets primarily to ensure that we are not biasing
analyses against the detection of significant, but comparatively brief,
regimes. In addition to conforming with general patterns in the NAO
(Hurrell 1995), ten years approximates one generation for northeast
Atlantic cod (in the absence of fishing), and should be sufficiently
long to detect persistent shifts in copepod abundance and water
temperature.

The second parameter of import is the hazard rate in the change point
prior, \selectlanguage{greek}λ. \selectlanguage{english}Lambda can be thought of as the probability or expectation of
the frequency of a regime shift, e.g., roughly every 10 years (\selectlanguage{greek}λ\selectlanguage{english}=10) or
every 25 years (\selectlanguage{greek}λ\selectlanguage{english}=25). This parameter is more challenging to base on
empirical expectation. Nonetheless, some caution in setting its value
can be exercised. Relatively small values of \selectlanguage{greek}λ \selectlanguage{english}(e.g., '10') might lead
one to falsely interpret short-term periods of seemingly extreme,
potentially spurious values as regimes. On the other hand, relatively
large values such as \selectlanguage{greek}λ\selectlanguage{english}=50 (regime shifts occurring twice in each
century) might be considered unduly `conservative', biasing against the
detection of biologically meaningful regime shifts because of the use of
a prior that constrains regime shifts to be comparatively infrequent.

For our analyses, we set \emph{M} =10 for all data sets. For the hazard
rate, we compare model outputs for \selectlanguage{greek}λ\selectlanguage{english}=10, 20, 25, and 50. Outputs for all
variables at alternative values of \selectlanguage{greek}λ \selectlanguage{english}are presented in the Supplementary
Information.

\emph{Data}

Our measure of biological productivity reflects the abundance of
juvenile Atlantic cod (ages 0+ to 2+ yr) in Skagerrak, a strait running
between the southeast coast of Norway, the west coast of Sweden, and the
Jutland peninsula of Denmark. Standardized beach-seine surveys have been
conducted along coastal Norwegian Skagerrak annually since 1919
(Stenseth et al. 1999). The time series of data available for our
analyses extended from 1919 to 2014.

In addition to cod, we examined time-series data for hypothesized
drivers of cod productivity. Winter NAO data (December through March)
were obtained for the years 1864 through 2018 (Hurrell et al. 2018). As
a measure of juvenile cod food supply, we tested for the presence of
regime shifts in the abundance of the energy-rich calanoid
copepod\emph{Calanus finmarchicus,} estimated by the Continuous Plankton
Recorder (CPR) survey for the survey area closest to, and overlapping
with, the Norwegian Skagerrak (area C1)
(https://www.cprsurvey.org/data/data-charts/) (Edwards 2019). We pooled
the CPR data for the months March through August, the period during
which zooplankton are available to, and consumed by, cod larvae and
juveniles in the North Sea (Nicolas et al. 2014). Sea-surface water
temperatures in Skagerrak are available from the Fl\selectlanguage{ngerman}ødevigen Research
Station, Institute of Marine Research
(http://www.imr.no/forskning/forskningsdata/temperatur\_flodevigen/draw.map?boey=1).
Temperatures recorded at Flødevigen are positively correlated with
temperatures elsewhere in Skagerrak (e.g., Fromentin et al. 1998). These
data were analysed on a monthly basis for the years 1925 to 2017.
Estimates of fishing mortality (\emph{F} ) and spawning stock biomass
(SSB) are available for North Sea cod, the management unit of which
Skagerrak cod is a part (ICES 2019).

\textbf{Results}

North Atlantic Oscillation

The BOCPD algorithm (at \selectlanguage{greek}λ\selectlanguage{english}=10 and \emph{M} =10) produces a pseudo-decadal
pattern in the winter NAO index, indicating that the model is capturing
the temporal dynamics previously ascribed to this index (Hurrell, 1995)
(Fig. 1a). Over the 140-year time series, ten regimes are identified.
Some, such as those between 1916 and 1960, are comparatively brief,
raising questions as to whether these patterns in the mean and(or)
variance in the data are consistent with some stipulations that regime
shifts represent stable states that are difficult to change (Scheffer
and Carpenter 2003; Conversi et al. 2015).

Taken together, these observations suggest that \selectlanguage{greek}λ\selectlanguage{english}=10 might represent an
unduly liberal frequency of break-point changes in the data, resulting
in a tendency to `over-identify' regime shifts. To guard against this
possibility, we steadily increased \selectlanguage{greek}λ \selectlanguage{english}to as high as 50 years. The model
output was identical irrespective of whether \selectlanguage{greek}λ \selectlanguage{english}was set at 20 or 25 years
(Figs. 1b,c). Four regimes were detected: 1864-1960 (97 yr); a negative
shift from 1961 to 1971 (11 yr); and a positive shift from 1972 to 1995
(24 yr), followed by a negative shift from 1996 to 2018 (23 yr). No
regime shifts were detected at \selectlanguage{greek}λ\selectlanguage{english}=50 (Fig. 1d), suggesting that this
hazard rate is unduly conservative.

Juvenile Atlantic Cod

At a hazard rate of \selectlanguage{greek}λ\selectlanguage{english}=10, seven regimes of cod catch rate were detected
from 1919 to 2014 (Fig. 2a). Despite some differences in the timing of
the shifts, they, as do all outputs from \selectlanguage{greek}λ\selectlanguage{english}=10 to 50, illustrate patterns
of substantive decline. However, there is reason to believe that a value
of 10 for the hazard rate yields regime shifts early in the data series
that should be interpreted with caution. The first thirty years are
characterized by highly variable catch rates. Data from the late 1930s
to the mid-1940s seem particularly suspect, given that catch rates
between successive years would normally be expected to be positively
(not negatively) autocorrelated (the juvenile cod group includes
primarily ages 0+ and 1+ yr). The 1939-1945 period coincided with WWII
during which fisheries research was greatly curtailed. We note that
other researchers (e.g., Fromentin et al. 1998) excluded this time
period from their analyses of the same beach-seine survey data because
sampling stations were few in number. Although we do not wish to exclude
data, we are disinclined to accept these unusual patterns of data
variability from the 1920s to the mid 1940s as reflecting valid regime
shifts (recall that the BOCPD algorithm recognizes changes in
variability, independent of the mean, as a basis for a regime shift).

As with the NAO index (Figs. 1b,c), \selectlanguage{greek}λ \selectlanguage{english}values of 20 and 25 detected
identical regimes (Figs. 2b,c) for the time-series of cod catch rate.
Four can be identified. The first two (1919-1952 and 1953-1974) differ
only in their variability, the former being more variable than the
latter. Catch rates for both regimes were \textasciitilde{}18.5 cod per
seine haul. However, catch rates during the third (1975-1998) and fourth
regimes (1999-2014) averaged \textasciitilde{}10 and \textasciitilde{}5
cod per haul, respectively. Comparing catch rates in the most recent
regime with those in the first two regimes, juvenile cod are estimated
to have declined more than 70\% since the early
20\textsuperscript{th}Century.

\emph{Zooplankton:} \textbf{Calanus finmarchicus}

Unlike the data on the NAO and cod, regime shifts in the abundance
of\emph{C. finmarchicus} changed little with changes in \selectlanguage{greek}λ \selectlanguage{english}(Fig. 3). At
hazard rates of 10 through 50, four regimes were distinguished. Focusing
on those at \selectlanguage{greek}λ\selectlanguage{english}=25, the earliest supported the highest average yearly
abundance of \emph{C. finmarchicus} in the time series, declining by
\textasciitilde{}75\% in the second regime (1982-1996). The yearly
abundance during the third regime (1997-2007) declined further still,
before increasing back to the level of the second regime during the
fourth regime (2008 to 2017).

Water Temperature

Data on water temperatures are presented as monthly averages (Figs. 4,
S1-S3). At \selectlanguage{greek}λ \selectlanguage{english}values of 20 and 25, the model outputs for the first half
of the year were remarkably similar, particularly at the higher hazard
rate (\selectlanguage{greek}λ\selectlanguage{english}=25). Two regimes were generally identified with a shift
detectable in 1988 for all months from January through June (Fig. 4).
The mean temperature increase between regimes ranged between
1\textsuperscript{0} and 2\textsuperscript{0}C. As with the first half
of the year, two regimes were generally distinguished from July through
December, again involving temperature increases of between
1\textsuperscript{0} and 2\textsuperscript{0}C (Fig. 4). Interestingly
the regime shifts (\selectlanguage{greek}λ\selectlanguage{english}=25) during the latter half of the year tended to
occur progressively later than those from January through June: July
(1997), August (1994), September (1996), October (1999), November
(2005), December (2014). The greatest increase occurred in August, with
mean temperatures between the first and second regimes increasing from
16.7\textsuperscript{0} to 18.7\textsuperscript{0}C.

Fishing Mortality and Spawning Stock Biomass

Regime shifts in juvenile cod abundance in Norwegian Skagerrak did not
occur in an environment in which cod mortality was affected solely by
natural causes. It is well established that fishing can dominate other
sources of change in the mean and variance of population size (Shelton
and Mangel 2011). In the present context, between 1963 and 2017, the
mean instantaneous rate of fishing mortality (\emph{F} ) on North Sea
cod aged 2-4 yr, of which Skagerrak cod are a part, was 0.82 (ICES
2019). By contrast, the average annual natural mortality of cod
comprising \textgreater{}90\% of the catch ranged between 0.2 (cod older
than 3 yr) and 0.74 (2-yr-old cod). Thus, since at least the early
1960s, fishing mortality experienced by North Sea cod has always
exceeded natural mortality.

Changes in fishing mortality (\emph{F} ) and the reproductive component
of North Sea cod (the spawning stock biomass, or SSB) can be expressed
relative to their limit reference points. When SSB falls below its limit
reference point (\emph{B\textsubscript{lim}} ), the population is
considered to have increased risk of impaired reproductive capacity
(ICES 2018). \emph{F} should not exceed
\emph{F\textsubscript{lim}}because such a level of prolonged overfishing
is thought to be associated with population dynamics that lead to stock
collapse. For North Sea cod, \emph{F\textsubscript{lim}} = 0.54. By
comparison, the fishing mortality corresponding to the maximum
sustainable yield (\emph{F\textsubscript{MSY}} ) is 0.31 (ICES 2019).

The BOCPD algorithm was applied to the fishing mortality data for North
Sea cod. Multiple regime shifts were detected and these were remarkably
similar at different hazard rates (Fig. 5). Stock assessment modelling
output indicates that fishing mortality on North Sea cod has rarely been
less than \emph{F\textsubscript{lim}} (Fig. 6), steadily rising from the
early 1960s through the late 1990s from 0.9
\emph{F\textsubscript{lim}}in 1963 to a maximum of 2.0
\emph{F\textsubscript{lim}} in 1999 (the year that initiated the second
Skagerrak cod regime shift). While\emph{F} steadily increased, stock
biomass experienced a decline from a peak SSB of 2.00
\emph{B\textsubscript{lim}} in 1971. By 1999, SSB was less than its
limit reference point (0.80 \emph{B\textsubscript{lim}} ), part of a
continuing decline that did not halt until 2006 when it had declined to
0.41 \emph{B\textsubscript{lim}} .

Temporal Overlap Between Regime Shifts in Cod Productivity and Putative
Drivers

Regime shifts were detected in multiple hypothesized drivers of cod
productivity. However, not all of these had obvious, or at least
immediate, consequences for cod. That is, regime shifts in NAO,
zooplankton abundance, and water temperature were not always followed
within 5 years by regime shifts in cod productivity (Fig. 6a).

The 1961 NAO regime shift (a decline from 0.1 to -2.0) had no
discernable impact, although the cod regime shift that began in 1974 was
preceded by regime-shift increases in both NAO (-2.0 to 1.5) and fishing
mortality (1.10 to 1.52 \emph{F\textsubscript{lim}} ). The initial
\textasciitilde{}75\% reduction in copepod abundance in 1981 followed,
rather than preceded, the 1974 shift in cod by 6-7 years (Fig. 6a).
Although the further reduction (\textasciitilde{}90\% decline)
in\emph{C. finmarchicus} in 1997 preceded the 1999 regime-shift decline
of cod (Fig. 6b), cod did not respond when zooplankton increased in 2008
back to its level in the 1981-1996 period. The nearly 50\% reduction in
average cod abundance that began in 1974 was not preceded by a regime
shift in water temperature in any month (Fig. 6a). However, the 1999 cod
regime shift either coincided with (October) or was preceded 2-5 years
earlier (July-September) by regime-shift increases in water temperature
of 1\textsuperscript{0} to 2\textsuperscript{0}C (Fig. 6b), reaching a
maximum monthly mean of almost 19\textsuperscript{0} C in August.

\textbf{Discussion}

The present study identifies regime shifts in a long-term metric of
biological productivity in relation to regime shifts in potential causal
drivers, using a Bayesian online change point detection (BOCPD)
algorithm. Juvenile Atlantic cod in Norwegian coastal Skagerrak
experienced two stepwise reductions in mean abundance, beginning in 1975
and 1999, ultimately attaining a level \textasciitilde{}30\% of what it
was in the first half of the 20\textsuperscript{th} Century. Regime
shifts in indices for the NAO and zooplankton abundance since 1960 were
directionally the same, the opposite, or independent of directional
shifts in cod catch rates. The degree of temporal overlap between
regimes shifts in cod abundance and water temperature depended on
season. Single regime shifts of increased mean temperature (by 1 to
2\textsuperscript{0}C) during the winter and spring months either
preceded the 1999 cod regime shift by more than a decade or occurred
several years thereafter. However, summer-autumn temperature regime
shifts (1 to 2\textsuperscript{0}C increase) were either concomitant
with, or occurred slightly in advance of, the cod regime shift
(decrease) in 1999. The earlier cod regime shift (1975) was not
associated with a regime shift in water temperature for any month of the
year.

The relative importance of hypothesized drivers can be ascertained by
the temporal proximity of their regime shifts with regime shifts in cod.
It is clear that shifts in some factors, such as the NAO index and
abundance of \emph{C. finmarchicus} , do not always have obvious
biological consequences for Atlantic cod. Against the background of
temporal changes in fishing mortality and spawning stock biomass of
North Sea cod, the earliest regime shifts in NAO (1961; a decline from
0.2 to -2.0) and \emph{C. finmarchicus} (1982; a \textasciitilde{}75\%
decline) were not linked with regime shifts in cod (Fig. 3a). The same
was true of the 1-2\textsuperscript{0} C regime-shift increase in water
temperature during the winter-spring months in 1988.

One interpretation of this lack of influence is that drivers of cod
productivity are less likely to manifest biological change when (i) they
act singly, (ii) human-induced mortality is relatively low, and (iii)
cod population size is relatively high. When the NAO shifted in 1961,
fishing mortality on North Sea cod was less
than\emph{F\textsubscript{lim}} and SSB was
1.36\emph{B\textsubscript{lim}} ; when zooplankton abundance shifted
downwards in 1982, fishing mortality was increasing but population
biomass remained high (1.53 \emph{B\textsubscript{lim}} ). Regarding the
winter-spring increase during the regime shift in water temperature that
began in 1988, it is notable that, despite these increases, temperatures
remained well within the range thought to be optimal for cod eggs and
larvae (Nissling 2004; Righton et al. 2010). Indeed, these January-June
regime shifts might have had a beneficial influence on cod productivity,
mitigating to some extent any steadily increasing effects of
persistently high fishing mortality and declining SSB.

Our analyses reveal two occasions when regime shifts in potential
drivers of cod productivity preceded regime shifts in cod catch rate by
a time period sufficiently brief (\emph{\textless{}} 5 yr) that they
could plausibly have influenced the subsequent abundance of cod aged 0+
to 2+ years (Fig. 6). Even though a decline in NAO in 1961 had no
discernable effect on cod, the increase in 1972 might well have, insofar
as the first cod regime shift followed two years later. This supposition
is supported by studies (e.g., Stige et al. 2006) that have concluded
that an increased NAO index has a negative influence on cod productivity
in the northeast Atlantic. One possible reason for why the NAO
apparently affected cod (beginning in 1974) is that the magnitude of the
NAO regime shift (-2.0 to 1.5) was the greatest of the three shifts that
occurred between 1864 and 2018. It is also notable, however, that the
1974 cod regime shift occurred during a period of steadily increasing
and unsustainably high fishing mortality (1.5\emph{F\textsubscript{lim}}
), potentially affecting the ability of cod to resist environmental
changes caused by the NAO, changes to which an unfished population might
have been resilient. This underscores the challenge in disentangling the
effects of fishing and climate-related indices on biological
productivity.

The cod regime shift that began in 1999 was preceded by a `perfect
storm' of multiple concomitant changes in the environment. Summer-autumn
temperatures jumped 1-2\textsuperscript{0} C; the NAO index declined
from 1.5 to 0.5; \emph{C. finmarchicus} had plunged to its lowest level
in the time series; fishing mortality was at its highest level since
1963 (2.0 \emph{F\textsubscript{lim}} ); and spawning stock biomass was
at its lowest level in the time series (0.8 \emph{B\textsubscript{lim}}
) en route to a minimum of 0.41 \emph{B\textsubscript{lim}} in 2006. The
effects of the NAO, \emph{C. finmarchicus} , and temperature on cod
productivity were undoubtedly accentuated by the directionality of their
regime shifts in 1999. As the NAO index declines, so does primary and
secondary productivity in Skagerrak (Tiselius et al. 2016), and
increased water temperatures are associated with increasingly
unfavourable conditions for \emph{C. finmarchicus} (Fromentin et al.
1998).

Among the putative drivers of cod productivity, the 1996 regime shift in
NAO may have been the most benign, given that (i) a reduction in the
index did not have its anticipated positive effect on cod and that (ii)
the index had returned to levels characteristic of the 1868 to 1960
period. The very considerable reduction in \emph{C.
finmarchicus}(beginning in 1997; Fig. 3) was likely a much more
prominent factor, given the exceedingly low levels to which this key
prey species of juvenile cod had declined.

There is, however, reason to believe that the summer-autumn increase in
water temperature was of considerably greater importance than either the
NAO or zooplankton abundance. Successive regime shifts from 1994 to 1999
during July through October raised temperatures to their highest
recorded levels in coastal Skagerrak since 1925, when the time series
began. In some years, mean August temperatures exceeded
20\textsuperscript{0}C, approaching the critical thermal maximum for
Atlantic cod (Righton et al. 2010; Norin et al. 2019).

We hypothesize that cod did not respond positively to the presumed
increased in food supply in 2008 because of the physiological stress
associated with increased summer-autumn water temperatures. Based on
tagging studies at sea of almost 400 cod from 8 northeast Atlantic cod
stocks, Righton et al. (2010) found that although the total thermal
niche of adult cod ranged between -1.5 and 19.0\textsuperscript{0} C,
the temperature range was considerably narrower during the spawning
period when larval and juvenile cod are developing (1 to
8\textsuperscript{0} C). Nissling (2004) reported that survival of
larval cod in the laboratory declined considerably when water
temperatures exceeded 10\textsuperscript{0} C.

One fundamentally important element to consider when evaluating the
consequences of climate-related and environmental regime shifts on
population productivity is the size of the population relative to a
metric of long-term sustainability, such as carrying capacity or
population size in an unfished state. This is because small populations
are more vulnerable to environmental stochasticity than comparatively
large populations (Lande 1993). This link between population size and
susceptibility to environmental change has been repeatedly considered
when assessing the recovery capacity of depleted cod populations
(Hutchings and Myers 1994; Hutchings and Kuparinen 2017). But it has
also been made with respect to potential drivers of cod regime shifts.
Based on an analysis of cod populations on the European Shelf south of
62\textsuperscript{o}N, including North Sea cod, Brander (2005)
concluded that environmental variability, as represented by the NAO
index, only affects cod when the spawning stock biomass is low.
Brander's (2005) argument is both theoretically compelling and
empirically supported by the present study.

There are several attributes to the methodology we have applied here.
Firstly, the same algorithm is used to identify regime shifts in a
metric of biological productivity and putative causal drivers of that
metric. Secondly, our approach greatly reduces the subjectivity inherent
in deciding the magnitude of data change which constitutes a regime
shift (the `effect' size) and when it is that a regime shift occurs; we
did not presume the existence of a regime shift in any given year for
any given variable. A third improvement is that the BOCPD algorithm
accounts for changes in the variance in the data, not simply the mean.

One limitation in our interpretation of the relative importance of
fishing and the environment on regime shifts in cod productivity is our
use of estimates of fishing mortality and spawning stock biomass for
North Sea cod as metrics of fishing pressure and population size for
Skagerrak cod. But if we were to account for fishing mortality in our
analyses, we needed to avail ourselves of the best available data in
this regard, and these data were available for North Sea cod. There are
empirically defensible reasons for our application of North Sea cod
estimates of \emph{F} and SSB to Skagerrak cod. Firstly, North Sea cod
genotypes exist along the Norwegian Skagerrak coast (Knutsen et al.
2018). Secondly, Skagerrak has long been considered part of the North
Sea cod stock unit (ICES 2019). Thirdly, limited estimates of fishing
mortality available for Skagerrak cod confirm that fishing mortality can
be exceedingly high. Kleiven et al. (2016) reported that recreational
and commercial fisheries for cod in Skagerrak fjords resulted in a
mortality rate of 55.6\% for the years 2005 to 2013, equivalent
to\emph{F} =0.81. For comparison, the average \emph{F} for North Sea cod
over the same time period was 0.61 (ICES 2019), suggesting that the
fishing mortality experienced by North Sea cod may be comparable to, and
possibly less than, that experienced by Norwegian Skagerrak coastal cod
in some years.

The concept of regime shifts permeates the marine ecological and
fisheries literature. Definitions vary considerably. The ecological
literature tends to interpret regime shifts as community-level changes
between alternative stable states with the implication that such shifts
are difficult to reverse (Conversi et al. 2015; Ling et al. 2015). In
contrast, regime-shift analyses of meteorological factors tend not to
focus on alternative stable states, being much more accepting of
regime-shift `reversibility' (e.g., Dippner et al. 2014; Jaagus et al.
2017). The fisheries literature is perhaps intermediate with respect to
the question of regime-shift reversibility. Some work draws attention to
long-term, slow-to-reverse discontinuities in ecosystem properties
(M\selectlanguage{ngerman}öllmann et al. 2009), whereas neither reversibility nor regime-shift
time period have been integral to a lack of temporal stationarity in
fish-stock productivity (e.g., Vert-pre et al. 2013; Perälä and
Kuparinen 2015).

Our analyses emphasize the utility in examining multiple regime shifts
when trying to understand the causal mechanisms responsible for regime
shifts in metrics of biological productivity. Doing so allows one to
formulate hypotheses and to draw conclusions concerning the conditional
probabilities that an environmentally related regime shift will affect
biological productivity. One hypothesis that emerges here is that the
strength of the effect of an environmental or climate-related regime
shift is accentuated when it coincides with other regime shifts. A
second hypothesis, underscoring the findings of previous work (Brander
2005; Hutchings and Kuparinen 2017), is that climate-related regime
shifts are more likely to affect populations when they are relatively
small. The present study affirms the dominant role that fishing has on
the probability that populations will respond to regime shifts in
environmental variables, underscoring the fundamental necessity of
accounting for fishing mortality in any analysis of regime shifts in
commercially exploited marine fishes (de Young et al. 2004; Möllmann et
al. 2009).

For our case study of Norwegian Skagerrak cod, our work suggests that
steadily increasing fishing mortality from commercial and recreational
fisheries has increasingly sensitized the cod to regime shifts in NAO,
zooplankton abundance, and water temperature. Fishing mortality remains
unsustainably high in the region (Kleiven et al. 2016). This, coupled
with small population size and increased summer and autumn water
temperatures that broach the thermal limit for the species, are likely
major factors limiting the recovery capacity for cod in southern coastal
Norway.

\textbf{Acknowledgements}

The authors are very grateful to the Sir Alister Hardy Foundation for
Ocean Science (SAHFOS, Marine Biological Association, Plymouth, UK, for
their permission to analyze data from the Continuous Plankton Recorder
Survey. We thank, in particular, Martin Edwards and David Johns of
SAHFOS. The research was supported by grants awarded by the Natural
Sciences and Engineering Research Council of Canada and Loblaw Companies
Limited to JAH, and the European Research Council (COMPLEX-FISH 770884
to Anna Kuparinen). The present study reflects only the authors' views
and that the European Research Council is not responsible for any use
that may be made of the information it contains.

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\textbf{Figure Captions}

\textbf{Figure 1.} Posterior predictive distributions of time series
data on the winter North Atlantic Oscillation (NAO) index. The units are
based on the difference of normalized~sea level pressure
between~Lisbon,~Portugal~and~Stykkisholmur/Reykjavík,~Iceland.
Differently shaded series of data represent different regimes. The
shaded area represents the 68\% central probability interval (CPI) of
the posterior predictive distribution; thus, it includes uncertainty
about the mean and the variance. Horizontal lines in each shaded region
represents the mean. \emph{M} is the minimum regime length (in years)
and \selectlanguage{greek}λ \selectlanguage{english}is the `hazard' rate in the change point prior, i.e., the
expectation of the frequency of a regime shift (a \selectlanguage{greek}λ \selectlanguage{english}value of 20 would
imply an expectation that regime shifts occur every 20 years).

\textbf{Figure 2.~} Posterior predictive distribution of juvenile
Atlantic cod catch rate (number of juvenile cod per beach-seine
haul).~See the caption for Figure 1 for explanations of the shaded
regions of the data.

\textbf{Figure~3.~} Posterior predictive distributions of data on the
abundance of~\emph{Calanus finmarchicus} ~as estimated from the
Continuous Plankton Recorder Survey (area C1).~Data have been pooled for
the months of March through August. Keeping~\emph{M~} constant at 10~yr,
model output is shown for~\selectlanguage{greek}λ\selectlanguage{english}~values of (a) 10, (b) 20, (c) 25, and (d) 50
years. See the caption for Figure 1 for explanations of the shaded
regions of the data.

\textbf{Figure~4.~} Posterior predictive distributions of data on sea
surface water temperatures measured at~Fl\selectlanguage{ngerman}ødevigen~Research Station for
the months of January through December at a hazard rate (\selectlanguage{greek}λ\selectlanguage{english}) of 25 years
(\emph{M~} = 10 years).~See the caption for Figure 1 for explanations of
the shaded regions of the data.

\textbf{Figure~5.~} Posterior predictive distributions of estimates of
instantaneous rate of fishing mortality (\emph{F} ) for cod aged
2-4~yr~in the North Sea. Hazard rate (\selectlanguage{greek}λ\selectlanguage{english}) is 10, 20, 25, and 50
years;~\emph{M~} is held constant at 6 years.~See the caption for Figure
1 for explanations of the shaded regions of the data.

\textbf{Figure~6.~} The timing of regime shifts in cod catch rate, NAO,
water temperature, and abundance of~\emph{Calanus finmarchicus} . Each
arrow identifies the beginning of a regime.~The direction of the arrow
indicates the change in the mean value of the data following each regime
shift. The timing of regime shifts is shown in relation to changes in
fishing mortality and spawning stock biomass of North Sea cod (each of
which is expressed relative to its respective limit reference point; the
limit fishing mortality is 0.54, the limit spawning stock biomass is
107,000 tonnes). (a) This panel identifies regime shifts in climate and
environmental indices that do not appear to have influenced regime
shifts in cod catch rate (i.e., were not followed within 5 years by a
cod regime shift). The water temperature regime in 1988 is for January
through June; the regime shift in 2005 is for November temperatures. (b)
This panel identifies regime shifts in climate and environmental indices
that do appear to have influenced regime shifts in cod catch rate (i.e.,
were followed within 5 years by a cod regime shift). The water
temperature regime shifts are for the months of August (1994), September
(1996), July (1997), and October (1999).\selectlanguage{english}
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