Estimation of change in lifetime egg production from length frequency data

The percentage of unfished lifetime egg production (LEP) has been used to represent persistence in precautionary fisheries management, but estimation of this reference point requires substantial data and it is sensitive to errors in natural mortality rate. We present an estimation method that quantifies the change in LEP by a fishery when only length frequency samples, one early in the fishery and one recent, are available for assessment. Using simulated length frequency data with known parameter values, estimates of LEP had undetectable bias when challenged with random sampling variability and sample sizes as low as 100. Simulation of artificial data with (i) growth parameters that differed from the estimation model, (ii) transient size structures, and (iii) recruitment variability led to predictably biased estimates. In a direct comparison with the spawning potential ratio reference point, fractional LEP was much less sensitive to errors in natural mortality rate. Application of this method to length frequency data for blue rockfish (Sebastes mystinus) for years between 1980 and 2003 suggests that during this interval, LEP has been reduced to levels of concern.