  The most commonly used relative abundance index in stock assessments of
longline fisheries is catch per unit effort (CPUE), here defined as the number
of fish of the targeted species caught per hook and minute of soak time.
Longline CPUE can be affected by interspecific competition and the retrieval of
unbaited or empty hooks, and interannual variation in these can lead to biases
in the apparent abundance trends in the CPUE. Interspecific competition on
longlines has been previously studied but the return of empty hooks is ignored
in all current treatments of longline CPUE. In this work we propose some
different methods to build indices to address the interspecific competition
that relates to empty hooks. We show that in the absence of information about
empty hooks, the relative abundance estimates have constant biases with respect
to fish density and this is typically not problematic for stock assessment. The
simple CPUE index behaves poorly in every scenario. Understanding the reasons
for empty hooks allows selection of the appropriate index. A scientific
longline survey is conducted every two years in the Strait of Georgia, British
Columbia by Fisheries and Oceans Canada. The above methods are applied to build
the time-series of indices from 2003 to 2009 for quillback rockfish (Sebastes
maliger). Due to variation in the incidence of non-target species, the index
trend obtained is moderately sensitive to the choice of the estimator.
