I recently published a technical note in Fisheries Research that described an algorithm for implementing the “seasonal cessation in growth model” of @Paulyetal1992. Describing an algorithm for a growth model does not seem like a useful contribution to the literature, as fitting growth models is pretty standard fare for fisheries scientists. However, fitting the @Paulyetal1992 model is complicated by the fact that the age data is modified by model parameters. This too may not seem particularly interesting given that $t_{0}$ in the typical von Bertalanffy growth function (VBGF) also modifies the age variable (i.e., $age-t_{0}$ appears in the VBGF equation). However, the modification of age in the @Paulyetal1992 model is a shift AND a compression of the age variable, AND the degree of shift and compression is a function of age. This is different, and more complicated, than the simple shift along the age axis in the typical VBGF.

As I demonstrate in my note, the @Paulyetal1992 model has, for all practical purposes, not been used in the fisheries literature. I believe that this lack of use is largely attributable to lack of clarity in how to implement the model in computer code.^[Note that @Paulyetal1992 did provide a brief description of their model, but not a detailed description of how the age variable was adjusted, and computer software for fitting their model, though that software, and its source code, have long been lost.] My hope is that the algorithm in my note will clarify the implementation of this model. Fisheries scientists can then rigorously test whether this model provides any advantage over other growth models with a seasonal component.

The paper is available here and full R code is available here. Implementation of the algorithm depends on my FSA package, which is available on CRAN. Please let me know what you think.