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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.

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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)