  Models of Stock Recruitment Relationships (SRRs) are often used to predict
fish population dynamics. Commonly used SRRs include the Ricker, Beverton-Holt,
and Cushing functional forms, which differ primarily by the degree of density
dependent effects (compensation). The degree of compensation determines whether
recruitment respectively decreases, saturates, or increases at high levels of
spawning stock biomass. In 1982 J.G. Shepherd united these dynamics into a
single model, where the degree of compensation is determined by a single
parameter, however the difficulty in relating this parameter to biological data
has limited its usefulness. Here we use a generalized modeling framework to
show that the degree of compensation can be related directly to the functional
elasticity of growth, which is a general quantity that measures the change in
recruitment relative to a change in biomass, irrespective of the specific SRR.
We show that the elasticity of growth can be calculated from short-term
fluctuations in fish biomass, is robust to observation error, and can be used
to determine general attributes of the SRR in both continuous time production
models, as well as discrete time age-structured models. This framework may be
particularly useful if fisheries time-series data are limited, and not
conducive to determining functional relationships using traditional methods of
statistical best-fit.

Populations and Evolution