Better catch curves: incorporating age-specific natural mortality and logistic selectivity

Catch curves are widely applied in data-poor fisheries but rely upon strong assumptions about constant fishing and natural mortality rates above some fully selected age.  We developed three novel catch curve methods that relax these assumptions by (1) estimating logistic selectivity parameters, (2) assuming Lorenzen-form natural mortality, or (3) both simultaneously.  We used simulation modeling to evaluate estimates of fishing mortality from conventional catch curves and our novel methods across a variety of data characteristics.  We also applied these catch curve methods to Atlantic menhaden (Brevoortia tyrannus) catch-at-age data, and compared catch curve estimates to 2010 assessment estimates of fishing mortality.  In our simulation modeling, catch curves that estimated logistic selectivity parameters performed better than conventional methods when logistic selectivity was present: this resulted in a 20% improvement in accuracy when the sample sizes for catch-at-age data were large.  In our example using menhaden data, logistic selectivity models provided estimates that were most similar to current stock assessment estimates.  Neither simulation nor real-world applications showed a large difference between constant and Lorenzen mortality models. We recommend our logistic-selectivity catch curves in studies where selectivity might be logistic because they improve accuracy at only a very small cost in computational complexity.