Piner et al.: Bias in estimates of growth when selectivity in models includes effects of gear and availability of fish 
79 
estimates of management quantities (Lee et al., 2017a) 
are being examined. Lee et al. (2017b) have shown 
the importance of accounting for age-based movement 
when estimating growth with random at-age methods. 
However, little research has shown the effects of ap¬ 
proximating age-based processes together with length- 
based ones (Lee et ah, 2017a). This article shows that 
the widespread application of estimated length-based 
selection in integrated assessment modeling argues 
that researchers are assuming unrealistic instanta¬ 
neous mixing, size-based movements, or are ignoring 
potential approximation biases. 
Our results apply even when fleet distribution cov¬ 
ers the entire stock area because the spatial distribu¬ 
tion of fishing mortality may not be the same as the 
spatial distribution of stock abundance. If spatial pat¬ 
terns in the stock are due to age-based movement, then 
the observed composition data and estimated selectivity 
would include age-based spatial patterns. Making mat¬ 
ters more complicated, as spatial patterns of the stock 
or the fishery change, the age-based availability of fish 
would also change annually (Lee et. al., 2017a). Simi¬ 
larly, the approximation bias is not confined to the esti¬ 
mation of growth. Even if an unbiased growth curve is 
specified in the assessment model, length-based models 
that do not correctly model both age- and length-based 
processes would still contain this approximation bias. 
Given the wide range of possible biotic and abiotic 
processes influencing fishery data, it may be difficult 
to provide a recipe for how best to approach the is¬ 
sues of estimating the growth of fish in fishery assess¬ 
ments. In situations with both age- and length-based 
processes impacting data, incorporating the relevant 
processes by using the correct biological units as part 
of the assessment model may provide the best option. 
Yet for length-based, age-structured assessment mod¬ 
els, estimating growth greatly complicates the analy¬ 
sis. Growth estimates may be confounded by estimates 
from other model processes (Maunder and Piner, 2015) 
and therefore require dubious assumptions, such as 
forcing asymptotic selectivity on a fleet. 
Analysts should give additional consideration to the 
estimation of growth when using only length-based se¬ 
lectivity. Modeling length-composition data is quite 
challenging, often requiring subjective choices about 
managing the inevitable misfit to these data (Francis 
2011; Lee et al., 2017a). These issues may be of greater 
importance for stocks assessed by using length-based, 
age-structured assessment models because of the im¬ 
portance that model predictions match observed length 
data. Research that is focused on understanding the rel¬ 
ative roles of length and age on many important fishery 
processes should be undertaken (McDaniel et ah, 2016). 
Acknowledgments 
The authors would like to thank several reviewers for 
helpful comments, as well as M. Maunder for guidance 
on this topic. 
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