15 
Statistical inference about the relative 
efficiency of a new survey protocol, 
based on paired-tow survey calibration data 
Email address for contact author: noel.cadigan@dfo-mpo.gc.ca 
1 Fisheries and Oceans Canada 
Northwest Atlantic Fisheries Center 
80 East White Hills Road 
St. John's, NL, Canada A1C 5X1 
2 Research and Evaluation Department 
Newfoundland and Labrador Centre for Health Information 
28 Pippy Place 
St. John's, NL, Canada A1B 3X4 
Abstract — Paired-tow calibration 
studies provide information on 
changes in survey catchability that 
may occur because of some necessary 
change in protocols (e.g., change in 
vessel or vessel gear) in a fish stock 
survey. This information is important 
to ensure the continuity of annual 
time-series of survey indices of stock 
size that provide the basis for fish 
stock assessments. There are several 
statistical models used to analyze the 
paired-catch data from calibration 
studies. Our main contributions are 
results from simulation experiments 
designed to measure the accuracy of 
statistical inferences derived from 
some of these models. Our results 
show that a model commonly used to 
analyze calibration data can provide 
unreliable statistical results when 
there is between-tow spatial varia- 
tion in the stock densities at each 
paired-tow site. However, a gener- 
alized linear mixed-effects model 
gave very reliable results over a 
wide range of spatial variations in 
densities and we recommend it for the 
analysis of paired-tow survey calibra- 
tion data. This conclusion also applies 
if there is between-tow variation in 
catchability. 
Manuscript submitted 20 April 2009. 
Manuscript accepted 14 September 2009. 
Fish. Bull. 108:15-29 (2010). 
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. 
Noel G. Cadigan (contact author ) 1 
Jeff J. Dowden 
Surveys are an important source of 
information for most fish stock assess- 
ments. They provide indices of abun- 
dance often used in mathematical 
models of the population to estimate 
absolute stock size and to provide 
future catch advice or to evaluate 
catch options for fishery managers 
(Kimura and Somerton, 2006). Survey 
indices are measures that we expect 
to be proportional to, or to indicate, 
stock size. The expected value of a 
random index R y available for year y is 
related to stock size (<S y ) by the model 
E(R v )=qS v The constant of proportion- 
ality, q, is usually referred to as the 
catchability of the index. Although we 
cannot directly infer stock size from 
a time series of indices R 1 , . . . ,R Y we 
can infer trends in stock size when 
q is the same each year. The survey 
observation is commonly referred to as 
a set (as in set the gear), or a tow when 
a trawl is used. The average survey 
catch for all sets provides an index of 
stock size. If the same survey proto- 
cols are used from year to year then 
the catchability of the index should 
remain relatively constant. The catch- 
ability may depend on length or age of 
fish, and we consider such extensions 
later in this article. 
There are many stock assessment 
models that are based on survey indi- 
ces (e.g., see Quinn and Deriso, 1999) 
and information on fishing and nat- 
ural mortality, to estimate absolute 
stock size. For most models it is neces- 
sary to have a fairly long time-series 
of survey indices, often 10 years or 
more. Over such time frames it may 
be necessary to change survey pro- 
tocols. This could be due to a need to 
replace the survey vessel, or to change 
gears for new priority species, etc. 
When such changes occur, it is use- 
ful to have information about how the 
catchability of the new survey protocol 
compares to the old protocol. 
Performing simultaneous paired- 
tow surveys using both protocols (e.g., 
old and new vessels, old and new fish- 
ing gears) provides direct data on 
how the catchabilities compare (e.g., 
Kimura and Zenger, 1997) Another 
approach is to simply fish side by 
side using both protocols and use the 
paired-catch data to estimate the ra- 
tio of catchabilities. We refer to this 
ratio as the relative efficiency, 
where q c and q t = the catchabilities 
of the old (control, 
c) and new (test, t) 
survey protocols. 
Notations are given in Table 1. If the 
fish densities entering both trawls are 
the same, or similar, and densities 
at different tow sites vary consider- 
ably, then for the same number of 
tows a paired-tow calibration study 
should produce better results than the 
