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.