The Structure of Complex Biological Reference Points and the Theory of Replacement

Abstract

AbstractThe percent spawning‐stock biomass per recruit (PSSBR) is a commonly used biological reference point (BRP). Justification for using specific values of PSSBR as BRPs has largely been based upon graphical interrelations of (1) the dependence of recruitment on stock, (2) the dependence of stock on recruitment (i.e., replacement), and (3) the dependence of spawning‐stock biomass on fishing mortality. This paper provides analytic solutions of these interdependencies. Analytic solutions are provided for equilibrium and nonequilibrium cases: (1) fixed recruitment and fixed mortality, (2) fixed recruitment and variable mortality, and (3) variable recruitment and variable mortality. The analysis is used to develop equations for both the “replacement line” and a full recruitment→stock→recruitment cycle. The analysis clarifies the connection between iteroparous and semelparous populations in both equilibrium and nonequilibrium settings. The analytic derivations provide the opportunity to conduct research on optimization of the equations and set the stage for field and laboratory studies of the dependence of stock on recruitment, complementing the much more intensive studies of the dependence of recruitment on stock.