Abstract
Natural mortality (M) rates are difficult to measure empirically and are often specified in stock assessments based on life history characteristics. More recently, these specifications have included M as a function of the size or age of a fish. However, natural mortality is a dynamic parameter that will change with the suite of predators and, thus, indirectly with cohort size and age. As an alternative, a density-dependent M rate function is derived and compared with the commonly used Lorenzen model, where M at age forms an allometric relationship with weight-at-age. The density-dependent model expresses M as a function of two parameters: one density dependent and one density independent. Properties of the two models (size-based vs. density-dependent) were explored to indicate conditions where the results are and are not similar. Associated catch equations, equilibrium analyses, and non-linear replacement lines in stock–recruitment theory are examined. Just as with density-independent values of M, most assessment data are not sufficient to provide precise estimates of density-dependent M parameters. However, the density-dependent model provides a basis for incorporating ecological variability into single-species assessments, noting the differing dynamics between short- and long-lived species. The incorporation of dynamic natural mortality has implications when estimating abundance trends and stock status, and ultimately setting management reference points.
Consistent thermodynamic treatment for a quark-mass density-dependent model
