Model parameters
There are two key parameters in the regime shift detection method. The
first is the minimum length of each regime, M (M =10 would
imply a minimum regime length of 10 year). For some data sets, Mcan 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 M =10.
In general, we can see a cogent argument for maintaining 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, λ. Lambda can be thought of as the probability or expectation of
the frequency of a regime shift, e.g., roughly every 10 years (λ=10) or
every 25 years (λ=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 λ (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 λ=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 M =10 for all data sets. For the hazard
rate, we compare model outputs for λ=10, 20, 25, and 50. Outputs for all
variables at alternative values of λ are presented in the Supplementary
Information.