In absence of systematic age reading of, for instance, otoliths, size frequency data may be used to estimate age compositions as a base for VPA or other procedures. In practice, however, this is not extensively done for most oceanic or developing country species or for most invertebrates. It may nonetheless be possible to use catch size composition and growth curves determined from biological sampling or tagging to gain rough estimates of total mortality at age and age/size at maturity. Various common criteria have been proposed for estimating mortality from size compositions (e.g. Sparre et al., 1989) which will not be entered into here, but Die and Caddy (1997) note that combining mortality estimates with size at maturity leads to an LRP criterion in terms of a Z-based LRP, Z*, defined by the inequality or limit:
Z* < K(Linf - Lm)/(Lm - Lc)
where Lm is the mean age at maturity. This inequality seeks to establish a limit in terms of conditions whereby a 50% chance of spawning at least once in the life history is assured, with the implication that, if not respected, due precaution is not being exerted.
The plot of total production against total mortality also yields a useful TRP, the point of Maximal Biological Production, which Die and Caddy (1997) show to be a relatively conservative TRP that corresponds to somewhat lower levels of fishing mortality than at MSY.
