Generalized compensation in stock-recruit functions: properties and implications for management

A general stock-recruit function that explicitly defines density-dependent and -independent components of mortality over multiple stages is derived. By generalizing the stock-recruit function and the timing of density-dependent compensation, the impacts of different sources and magnitudes of mortality during the recruitment phase can be evaluated. Given reasonably comparable stage durations, compensation in early stages of a multistage process dominates density-independent effects, in later stages, density-dependent and -independent factors compete on a more even scale. Ratios of equilibrium statistics associated with the stock-recruit function under alternative compensation timing scenarios can be determined from the ratio of the compensation terms in the models when all scenarios assume the same type of stock-recruit function (Ricker or Beverton-Holt). This analytical result facilitates evaluation of proposed impacts or rehabilitation strategies without the need for a full stock assessment. Exogenous mortality has more impact on the maximum excess recruitment if that rate occurs later in the recruitment interval, especially if it takes place after compensation. Reparameterizing this generalized stock-recruit function in terms of steepness and virgin recruitment, we show that steepness is not influenced by the timing of compensation nor by the length of the recruitment interval; the level of virgin recruitment, however, is affected by both.