75 
National Marine 
Fisheries Service 
NOAA 
Fishery Bulletin 
fa- established in 1881 ~<f> 
Spencer F. Baird 
First U S Commissioner 
of Fisheries and founder 
of Fishery Bulletin 
Bias in estimates of growth when selectivity in 
models includes effects of gear and availability 
of fish 
Email address for contact author: kevin.piner@noaa.gov 
' Southwest Fisheries Science Center 
National Marine Fisheries Service, NOAA 
8901 La Jolla Shores Drive 
La Jolla, California 92037 
2 Bren School of Environmental Science and Management 
University of California Santa Barbara 
2400 Bren Hall 
Santa Barbara, California 93106 
Abstract-Stock assessment models 
use data influenced by distribution 
patterns that are due to the nonran¬ 
dom movement of fish, which can 
create bias in the assessment. For 
many stocks, length data are used 
to characterize the age structure of 
the population, and therefore there 
is a need for unbiased estimates of 
growth. Because of the influence of 
size-selective fishing gear, growth 
and length-based selectivity are 
often estimated as part of an as¬ 
sessment model to account for the 
size selection of gear. However, es¬ 
timated selectivity can include not 
only length-based gear selection, but 
the biological aspects of the spatial 
availability of the target species. If 
availability to the fishing gear is a 
function of age, an approximation 
of an age-based process as a length- 
based one can bias growth estimates. 
The magnitude of the bias would be 
greater for fish with highly variable 
growth and for those with strong 
age-based distribution patterns. 
Manuscript submitted 14 June 2017. 
Manuscript accepted 7 November 2017. 
Fish. Bull. 116:75-80 (2018). 
Online publication date: 22 December 2017. 
doi: 10.7755/FB.116.1.8 
The views and opinions expressed or 
implied in this article are those of the 
author (or authors) and do not necessarily 
reflect the position of the National 
Marine Fisheries Service, NOAA. 
Kevin R. Finer (contact author) 1 
Hui-Hua Lee 1 
Lennon R. Thomas 2 
Spatial patterns in the distribution 
of sizes and ages of fish (patterns 
due to the behavior of fish) are com¬ 
mon. Because movement rates may 
be difficult to estimate as part of a 
population dynamics model (Lee et 
al., 2017a), the spatial patterns in 
size or age are often modeled implic¬ 
itly as selectivity (Hurtado-Ferro et 
al., 2014; Waterhouse et al., 2014; 
Lee et al. 2017a). Implicit treatment 
of spatial patterns uses the model 
estimate of the selectivity process to 
represent both spatial availability, 
as well as the selectivity of the gear 
(Maunder et al., 2014). Gear selectiv¬ 
ity represents the probability that a 
fish is captured when it encounters 
the gear, whereas availability is the 
probability that a fish will encounter 
the gear. It is common practice to 
estimate fleet selectivity as a func¬ 
tion of fish length (Crone and Valero, 
2014) because it is generally assumed 
that gear selectivity is related to fish 
size (Stewart, 1975; Yanase et al., 
2007), whereas availability due to 
movement could be a function of size 
(Npttestad et ah, 1999) or age (Fran¬ 
cis, 2016; McDaniel et al., 2016). 
Length-based, age-structured mod¬ 
eling is used for many migratory fish 
stocks because routine age determi¬ 
nation of fishery samples is not al¬ 
ways provided. In these assessment 
models the length composition data 
are used to approximate the age 
structure of the catch. To use the ob¬ 
served lengths reliably, an unbiased 
estimate of the length-at-age rela¬ 
tionship is needed. Unless properly 
accounted for, the processes of avail¬ 
ability of fish and gear selectivity 
can cause bias in comparisons with 
the actual total population, which 
can bias estimates of growth (Finer 
et al., 2016; Lee et ah, 2017b) and 
ultimately the management of catch 
quotas (Maunder and Piner, 2017). 
Age-length data used to estimate 
growth must satisfy at least one of 
two assumptions depending on how 
they are used (Francis, 2016). With 
the random-at-age method for esti¬ 
mating growth, lengths are assumed 
to be random with respect to age. Es¬ 
timates from this method can be bi¬ 
ased without a proper accounting for 
length-based processes (e.g. length- 
based gear selectivity). Length-at-age 
