Estimating persistence of fished populations with limited data

The population dynamic consequence of individuals producing sufficient progeny over their lifetime for replacement is sustainability. Exploited marine populations experience elevated mortality rates due to fishing, with the result being a truncation of age structure, size structure and lifetime reproduction. This loss of old, large individuals causes a decrease in Lifetime Egg Production (LEP), the number of eggs produced by an individual over a lifetime, and a reduction in the ability of an individual to replace itself. Estimation and maintenance of a threshold level of LEP is thus a central focus of fisheries management. The method developed here for estimating the fractional change in LEP (FLEP) from two length frequency distributions, one early in the exploitation history and one recent, allows for inference about the changes in LEP owing to a fishery with a minimum amount of data. The FLEP estimation method was found to be unbiased at low sample sizes, but could be predictably biased in cases where assumptions of the model were violated. The method performed better than conventional means of estimating changes in LEP as it was nearly insensitive to the highly uncertain natural mortality rate parameter. Application of the FLEP estimation method to 23 years of length frequency data for 5 species of rockfishes (Sebastes spp.) in California and Oregon suggested that LEP has been reduced to levels of concern for 4 of the 5 species. In addition, large differences in LEP were estimated over space, implying that fishing mortality is not evenly distributed. Finally, the efficacy of managing fisheries by estimating LEP was evaluated in a modeling study for populations where maternal age dependence on larval mortality exists. In general, the effect of high mortality rates for larvae produced from young females results in small assessment errors if the contrast in larval mortality rate exists only for the youngest spawners, which contribute a small proportion of the total egg and larval production. Evaluation of a specific example for black rockfish (Sebastes melanops) suggests that maternal age effects would produce relatively small assessment errors if LEP were used for assessment.