Stock-production functions resembling Beverton-Holt

Abstract

Researchers dissatisfied with the performance of the Beverton-Holt model, in contexts where \"Beverton-Holt-like\" behavior is expected, have introduced a plethora of alternative model forms. This paper presents a formalization of what constitutes \"Beverton-Holt-like behavior\" which includes many of these forms, and shows that the class of functions so defined has a coherent and non-trivial mathematical theory. Data from the stock production database assembled by Ransom Myers is used to illustrate why such generalizations have been sought in the first place, and to highlight the difficulties in choosing between model forms on purely empirical grounds. Special attention is given to a parametric family of functions within this class, here called \"{theta}-BH\" functions. These functions cover a broad range of shapes, including both the Beverton-Holt and hockey stick functions, and share useful properties with these two widely-used models.