Revise section on Richards growth function #269
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e-perl-NOAA
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Dec 5, 2024
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Thanks much Arni for this excellent contribution. |
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In light of the findings of Arni and Ian analyzing the Richards growth function in Stock Synthesis (draft vignette) and a related question by Larry Jacobson on the Gompertz growth function (forum message), I would like to propose a revised text for the Richards growth function in the User Manual.
This pull request makes the following changes:
Refer to "Richards" rather than "Schnute/Richards" growth function, to simplify and acknowledge that the Schnute parametrization (1981, Eq. 15) produces the same curves as other Richards parametrizations. Also to prevent confusion with the five-parameter Schnute-Richards (1990) growth function, which is quite different.
Replace the rather old and vague text that "when this function was first introduced, it was required that the A0 parameter be set to 0.0" with similar guidance that "when A1 is greater than the youngest age in the model, some combinations of Richards growth parameters can lead to undefined (NaN) predicted length for the younger ages".
No longer refer to b<0 as the "Richards" model and b>0 as the "generalized von Bertalanffy" model. In modern parlance, all values of b are the Richards model. The models referred to as Richards growth models by Tjorve and Tjorve (2010) and the FSA package produce the same curves as the Schnute (1981, Eq. 15) function that is used in Stock Synthesis.
Guide the user that b should not be set to precisely 0 and that to use the Gompertz growth function, the user can fix the Richards shape parameter at a small value such as b=0.0001. The main Richards equation still applies and there is no real need for showing the equivalent Schnute (1981, Eq. 16) case 2 (Gompertz) function that is not implemented in Stock Synthesis.
Omit the somewhat unclear guidance that it might be necessary to constrain b to "different ranges". In practice, b will probably be somewhere between -3 and +6, as shown by the corresponding growth curves in the vignette.
Last, but not least, mention that the SS3 website includes a vignette providing further technical insights for using the Richards growth model in Stock Synthesis.