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How much sampling coverage affects bycatch estimates in purse
seine fisheries ?
Amand`e, M. J.a,b, Lennert-Cody, C. E.c, Bez, N.b, Hall, M. A.c, Chassot, E.b
aUniversit´e de Montpellier 2, Place Eug`ene Bataillon, 34090 Montpellier, FRANCE
bInstitut de Recherche pour le D´eveloppement, CRHMT - UMR 212, Avenue Jean Monnet, BP 171,
34200 S`ete cedex, FRANCE
cInter-American Tropical Tuna Commission, 8604 La Jolla Shores Drive, La Jolla, CA 92037-1508,
U.S.A.
Abstract
IOTC-2010-WPEB-20 presents the results of a simulation approach conducted to eval-
uate the biases and uncertainties associated with the use of a ratio estimator method
to estimate bycatch in tropical tuna purse seine (PS) fisheries. Simulations were based
on a set of observer data collected in the Eastern Pacific Ocean by IATTC in 2000 and
focused on fishing sets made on floating objects and on 4 major bycatch species: mahi
mahi (Coryphaena hippurus), silky shark (Carcharhinus falciformis), swordfish (Xiphias
gladius), and blue marlin (Makaira nigricans). Results mainly showed that biases and
uncertainties were strongly dependent on the percentage of coverage as well as on the fish
species considered. The current 10% sampling coverage rate of the European PS fishery
of the Indian Ocean would lead to positives biases (<5%) and large uncertainties (>
20%) in bycatch estimates for the 4 species when caught on log-associated schools. The
importance of the fishery, i.e. total number of trips, was also shown to affect bycatch
estimates for a specific level of sampling coverage. The use of unbiased ratio estimators
was found to be particularly useful when sampling coverage is low (<10%).
Keywords: Bycatch, simulation, ratio estimator, bias, uncertainty
∗Corresponding author
Email address: amonin2@yahoo.fr (Amand`e, M. J.)
Working Party on Ecosystem and Bycatch IOTC-2010-WPEB-20
1. Introduction
Incidental catch of non target marine animals is a general and increasing concern in
world marine fisheries (Hall 1998, Gaertner et al. 2002, Kelleher 2005, Minami et al.
2007, Soykan et al. 2008). One common and simple approach to compare the magnitude
of bycatch within or between fisheries is to express their bycatch as a function of target
species catch or the fishing effort (Hall 1999). Bycatch rate could be an important
indicator to evaluate the relative impact of each fishery on a given non target species
(Watson et al. 2008). Unfortunately this indicator is in general not calculable from usual
fishery data (logbook) because information about non target species is not available or
poorly mentioned by fishing masters (Gaertner et al. 2002).
Observer data have been shown to be a unique opportunity for scientists to learn more
about species that are incidentally caught by fishermen (e.g. Amand`e et al. 2009). Then,
the expression of bycatch over catch or effort, called ratio is in general calculated from
observer data and generalized to the whole fisheries from which the observer data are
supposed to derive (De Pascual 1961, Rochet and Trenkel 2001, Kadilar and Cingi 2003,
Borges et al. 2005, Sims et al. 2008) because of its simplicity and practical use. However,
bycatch estimation remains still problematic in fisheries in which observer data represent
a small part of the total fishing activities (Tsitsika and Maravelias 2008, Hall 1999, Law-
son 2001) because of the the skewness and/or high variability in bycatch distribution.
While the magnitude of bias and uncertainty in bycatch estimates could seriously impact
decisions for fishery management, these notions are rarely mentioned in reviewed papers
on bycatch estimation (Babcock et al. 2003).
The purpose of this paper is to analyze the effects of sample size in terms of bias and
2
uncertainty on bycatch estimates in purse seine fisheries using a simulation approach.
2. Materials and methods
Data
Data were collected by observers aboard tuna purse seiners within the framework of the
observer programme conducted in the eastern Pacific Ocean (EPO) by the Inter-American
Tropical Tuna Commission (IATTC). IATTC data used here are only from floating objects
sets collected in 2001 and represent 449 observed trips and 5,613 sets. Nearly 100% of the
trips were observed in the IATTC observer programmme of which floating objects sets
represented almost 85%. The term ”bycatch” herein refers to incidental species caught
during purse seine operations and the ”catch” will refer to the retained catch of target
tuna species, i.e yellowfin Thunnus albacares, skipjack Katsuwonus pelamis, and bigeye
Thunnus obesus. Four species with different characteristics were selected for this study
(Table 1). Details about the IATTC observer programme can be found in Hall (1995),
Lennert-Cody et al. (2004), Watson et al. (2008), Lennert-Cody et al. (2008).
Approach
The fishing trip has been shown to be the best sampling unit for bycatch estimation
Borges et al. (2005) and represents the real statistical unit on which sampling design
could be made in purse seine fisheries. Simulations were then conducted at the trip level.
For simulation purpose, the total observed data was considered as the fishery universe,
i.e logbook data and simulation consisted in simple resampling without replacement in
that population universe. It means that observer data were created by simple random
sampling in the population trips. Ratio estimator was based on tuna catch and effort
3
as auxiliary variables because such informations is always available in logbook data and
generally used for raising procedures.
Bias in bycatch estimate
The simulation approach used here for quantifying bias and uncertainty in bycatch
estimate was proposed by Babcock et al. (2003) and formulas mentioned in this section
could be found in Thompson (2002).
5,000 observer samples were randomly drawn from logbook data under various levels of
coverage (sequential from 5% to 100%). Let,
yt, and xtdenote observer bycatch and tuna catch values per trip, respectively;
µy,µx, the population mean bycatch and mean catch (or number of sets), respec-
tively;
Nand n, the number of trips in logbook and observer data, respectively.
The population ratio Rcalculated from logbook data and the sample ratio rfrom each
simulated data were defined as:
R=µy
µx
and r=
n
X
t=1
yt
n
X
t=1
xt
(1)
The relatives bias (relB) and root mean square error (relRM S E) were calculated for
each coverage level and each bycatch species using equation 2 and equation 3; where E(r)
is the expectation of the ratio obtained from the 5,000 bootstrap samples.
4
relB =E(r)−R
R(2)
relRM SE (r) = pE(r−R)2
R(3)
The relative values of bias and root mean square error are preferred to the absolute
values in order to compare results obtained on the basis of the effort and the catch taken
as auxiliary variables.
Uncertainty in bycatch estimates
Using a Taylor series expansion of this simple ratio, i.e raround µyand µx, van Kem-
pen and van Vliet (2000) demonstrated that the ratio used above is only asymptotically
unbiased and proposed an approximate expression of the unbiased ratio as follows:
rv=¯y
¯x−1
nµy
µ3
x
var(x)−cov(y, x)
µ2
x(4)
Bootstrap approximation of rv
Ratio is used in general as raising procedure because the amount of non target species is
only known at the sample level. In fishery real-life data, the population total bycatch is
not available. This means that in practice, Equation 4 is not directly calculable because
µyis unknown. We used bootstrap approach to derive an unbiased estimation (µ∗
y) of the
bycatch average per trip using observer data. Equation 4 becomes 5.
r∗
v=¯y
¯x−1
nµ∗
y
µ3
y
var(x)−cov(y, x)
µ2
y(5)
We finally compare the performance of the three ratio estimators (r,rvand r∗
v) to the
5
real ratio (R) on the basis of their average value estimated from the 5,000 samples.
3. Results
Magnitude of bias and uncertainty in bycatch estimates
The results obtained by using the effort as auxiliary variable were similar to those
obtained by using the catch, for all species. Only the relative bias of the mahi-mahi was
different with a correlation of 0.4 (Table 2). The simple ratio estimator induced bias and
uncertainty in bycatch estimates. The magnitude of bias and variability were strongly
dependent on the bycatch species and the sampling coverage (Figures 1-2). Swordfish was
the less predictable bycatch with the highest bias and uncertainty on the estimates. Both
bias and uncertainty were shown to be inversely proportional to the sampling coverage
with a logarithmic trend for uncertainty (Figure 1). While the magnitude of bias seemed
relatively low (less than ±5%) for all species, the error on the estimates were relatively
high, particularly for low sampling. This uncertainty on bycatch estimates was between 10
and 50% when coverage rate was smaller than 20% for silky, mahi-mahi and blue marlin;
however swordfish estimates was highly unprecise whatever the level of sampling coverage.
The bias and precision in bycatch estimates depended on the sampling coverage and the
importance of the fishery (Figure 3). For the same sampling coverage, estimates were less
precise in small fisheries, i.e with the lowest number of trips. This means the coverage rate
is not a sufficient factor that impacts the precision in bycatch estimates. The absolute
number of observed trips also matters.
6
Comparison of estimators
The expectation of the simple ratio estimator was distinct to the true value of the ratio R
when sampling coverage was less than 30%. The bias induced by this ratio estimator was
positive in general, meaning that the biased ratio roverestimated bycatch. The expection
of the simple ratio was different to the others (rv, r∗
v) which were very close (Figure 4).
Howerer the three estimators (r, rv, r∗
v) described above seemed very similar when the
sampling coverage was less than 30%. The bootstrap approximation of the unbiased ratio
estimator (r∗
v) seems comparable to rvwhen sampling coverage reaches 5%.
4. Discussion
Only observer data collected in 2000 on fishing sets made on floating objects were used
in the present analysis for reasons of homogeneity. Hence, we expected to avoid temporal
(i.e. annual) and fishing mode effects within the simulation procedure. Simulation results
could then differ if they were based on another dataset. The magnitude of bias and
uncertainty in bycatch estimates would certainly be higher than those obtained here had
we considered sets made on free swimming schools because bycatch tends to be rare in
free swimming schools sets (e.g. Amand`e et al. 2009).
Our results showed that using the catch or the effort as auxiliary variable did not affect
the precision and bias in bycatch estimates. This is due to the fact that total tuna catch
per trip was proportional to the number of sets per trip in the data considered in this
analysis. Our results differ to those obtained by Amand`e et al. (in press) in which raising
procedure was done at the set level. However, the true statistical unit is the trip (Borges
et al. 2005). Conducting the analysis at trip level (re-sampling trips rather than sets)
7
is also consistent with the practical aspects of observer sampling design in purse seine
fisheries.
The ratio proposed by van Kempen and van Vliet (2000) is an ”unbiased” expression of the
simple ratio obtained by using a second order of Taylor series expansion. This estimator
remains still quite biased for a low coverage rate because it remains a mathematical
approximation. However this approximate ratio gave best results compared to the simple
ratio estimator. In practice the formula proposed by van Kempen and van Vliet (2000)
is not directly useful for estimate bycatch. Bootstrap approach could be used to obtain
similar results as what was expected when using the unbiased ratio estimator.
5. Conclusion
We showed that bias and uncertainty in bycatch estimates depend on the species, sampling
coverage, and the absolute number of trips made at the level of the whole fishery. The
fishery importance combined with the sampling coverage represents the absolute number
of observed data that will be considered when planning observer programme for bycatch
assessment. In our case, tuna catch used as auxiliary variable gave similar results in terms
of bias and uncertainty as the fishing effort expressed in numbers of sets. Because bycatch
estimates highly depend on the species distribution, it is of major importance to correct
for bias and provide precisions associated with bycatch estimates.
6. Acknowledgments
We thank IATTC administrators and scientists, particularly Nick Vogel for his
wonderful work on observer database management. We are grateful to Lau-
8
rent Dagorn (IRD) for his collaboration. This work was financially sup-
ported by the IRD-DSF (http://www.ird.fr/les-partenariats/soutien-et-formation-des-
communautes-scientifiques-du-sud) and the European project MADE (http://www.made-
project.eu).
9
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Table 1: Characteristics of non target species selected for the simulation tests
Specie scientific name Common name Characteristics
Coryphaena hipurus Mahi mahi One of the most species in tuna fisheries
with common characteristics between fish-
eries. Mahi mahi occurs in 85% of sets but
the number of individuals caught is highly
dispersed and can vary from 1 to more than
2000 individuals.
Carcharhinus falciformis Silky shark The most frequent species of elasmobranches
in purse seine fisheries with about 1/3 of pos-
itive occurrence in their catch per set. The
distribution of silky shark per set is skewed
and overdispersed. (See Minami et al. (2007),
Amand`e et al. (2008), Watson et al. (2008), Ro-
manov (2008) for more details).
Xiphias gladius Swordfish Rare in purse fisheries (>99% of zeros) with
low variance. The number of swordfish ob-
served per set is always low (more than 99%
of observations don’t exceed 3 individuals)
when positive occurrence.
Makaira nigricans Blue marlin The blue marlin could be considered as mid-
dle occurrence specie in purse seine fisheries
i.e more frequent than swordfish and less
than silky shark. But in contrary to sword-
fish the number of individuals can attend 10
inviduals.
Table 2: Correlation between results obtained using effort or using the catch as auxiliary variable.
Specie Relative Bias Relative mean square error
Mahi mahi 0.4 1.0
Silky shark 0.9 1.0
Blue marlin 0.8 1.0
Swordfish 0.9 1.0
13
Coverage (%)
20 40 60 80 100
0%
10%
20%
30%
40%
50%
Mahi mahi
Silky shark
Blue marlin
Swordfish
Figure 1: Uncertainty in bycatch estimate as a function of sampling coverage
Coverage (%)
20 40 60 80 100
−5%
0%
5%
10%
Mahi mahi
Silky shark
Blue marlin
Swordfish
Figure 2: Bias in bycatch estimate as a function of sampling coverage
Silky shark
Coverage (%)
20 40 60 80 100
−20%
−10%
0%
10%
20%
30%
40%
50%
MSE in Fishery 1
MSE in Fishery 2
MSE in Fishery 3
MSE in Fishery 4
Rel. Bias in Fishery 1
Rel. Bias in Fishery 2
Rel. Bias in Fishery 3
Rel. Bias in Fishery 4
Mahi−mahi
Coverage (%)
20 40 60 80 100
−20%
−10%
0%
10%
20%
30%
40%
50%
MSE in Fishery 1
MSE in Fishery 2
MSE in Fishery 3
MSE in Fishery 4
Rel. Bias in Fishery 1
Rel. Bias in Fishery 2
Rel. Bias in Fishery 3
Rel. Bias in Fishery 4
Figure 3: Bias and uncertainty as a function of observer coverage and importance of fisheries. Fisheries
1,2,3 and 4 have 449, 225, 150 and 113 trips, respectively.
0.0 0.1 0.2 0.3 0.4 0.5
3.5 3.6 3.7 3.8 3.9 4.0
coverage
0 45 90 135 180 225
Number of trips
R
r
rv
rv*
Figure 4: Comparison between the simple ratio (r), the unbiased ratio (rv) proposed by van Kempen
and van Vliet (2000) and the bootstrap approximation of the unbiased ratio (r∗
v)
