Reprint of “Estimating tag reporting rates for tropical tuna fleets of the Indian Ocean”

G Model

ARTICLE IN PRESS

FISH-3910; No. of Pages 13

Fisheries Research xxx (2014) xxx–xxx

Contents lists available at ScienceDirect

Fisheries Research journal homepage: www.elsevier.com/locate/fishres

Reprint of “Estimating tag reporting rates for tropical tuna fleets of the Indian Ocean”夽 T. Carruthers a,∗ , A. Fonteneau b , J.P. Hallier b a

Fisheries Centre, AERL, University of British Columbia, 2202 Main Mall, Vancouver, BC, Canada V6T 1Z4 Unité Mixte de Recherche 212 Ecosystèmes Marins Exploités, Institut de Recherche pour le Développement, Centre de Recherche Halieutique, Méditerranéenne et Tropicale, BP 171, 34203 Sète Cedex, France b

a r t i c l e

i n f o

Article history: Received 30 May 2013 Received in revised form 8 October 2013 Accepted 13 February 2014 Available online xxx Keywords: Reporting rate Indian Ocean Tropical tuna Bayesian Tagging Mark-recapture

a b s t r a c t Estimates of tag reporting rates are necessary in order to estimate tag-recovery rates and interpret tagging data in terms of movement rates, exploitation rates and abundance. We describe a Bayesian framework for the estimation of reporting rates for multiple fleets using coincidental tagging and catch data disaggregated by fish size, species, location and time. The method was applied to the data of the Indian Ocean Tuna Tagging Programme (2006–2011) and tag seeding experiment of the Indian Ocean Tuna Commission (2004–2009). Reporting rates were estimated for 13 Indian Ocean tuna fleets. These estimates varied widely from 94% for the European Union purse seine fleet to less than 1% for fishing operations of non-longline/non-purse seine fleets in the Eastern Indian Ocean. Generally, reporting rates were high compared with estimates for tuna fisheries in other Oceans. © 2014 Elsevier B.V. All rights reserved.

1. Introduction In the year 2000, a large-scale tropical tuna tagging programme was initiated in the Indian Ocean (The Indian Ocean Tuna Tagging Project, IOTTP). By 2009 over 200 000 fish had been tagged using both conventional and electronic tags. To date over 32 000 tags have been recovered. The three principal tropical tunas (skipjack, Katsuwonus pelamis; yellowfin, Thunnus albacares and bigeye, Thunnus obesus) were targeted in two distinct tagging programmes: a smallscale tagging operation (from March 2002 to April 2009) and the Regional Tuna Tagging Project (RTTP) from 2005 to 2009. The RTTP was the principal component of the IOTTP and was responsible for 83.5% of the tag releases and 87.8% of the tag recoveries (Hallier and Million, 2009). The RTTP was implemented by the Indian Ocean Commission (Mauritius) and coordinated by the Indian Ocean Tuna Commission (IOTC, Seychelles). From May 2005 to August 2007, the RTTP chartered two pole and line vessels and tagged tuna in the Western Indian Ocean ranging from the East African coast to the Seychelles, the Arabian Sea in the North to the Mozambique

DOI of original article: http://dx.doi.org/10.1016/j.fishres.2014.02.011. 夽 This article is a reprint of a previously published article. For citation purposes, please use the original publication details “Fisheries Research” 155 (2014) 20–32. ∗ Corresponding author. Tel.: +1 604 822 6903; fax: +1 604 822 8934. E-mail address: t.carruthers@fisheries.ubc.ca (T. Carruthers).

Channel in the South. The small-scale release project covered fisheries that could not be reached by the RTTP, for example in the waters of the Maldives, India and Indonesia. A well-publicised tag recovery scheme was implemented around the Indian Ocean to cover all sectors involved in the fishing, marketing and processing of the three targeted tuna species. The overall objective of the IOTTP was to (1) reinforce the regional management capacity, to support the sustainable exploitation of tuna resources in the Indian Ocean, (2) improve the scientific basis for the stock assessment of Indian Ocean tropical tuna stocks in order to better characterise the rate of exploitation. This paper is concerned with the second objective. In order to use tagging data to estimate exploitation rates it is first necessary to quantify the factors that determine the probability of recapturing a tag such as natural mortality, tag-induced mortality, tag shedding, tag failure and tag reporting (see the series starting Pollock et al. (2001) for a review of methods of estimating reporting rate). Of these factors, reporting rate is likely to be the most influential in determining the number of tags that are eventually recorded in a tag recapture database. For example, Carruthers and McAllister (2010) estimated reporting rates of less than 1% for Atlantic tuna fleets while Pollock et al. (2002) estimate reporting rates in the range of 24–95% in the Southern bluefin tuna fishery. Kimura (1976) identified an approach to estimating reporting rates of all fishing operators by knowing the reporting rate of one operator. Carruthers and McAllister (2010) developed a Bayesian

http://dx.doi.org/10.1016/j.fishres.2014.07.002 0165-7836/© 2014 Elsevier B.V. All rights reserved.

Please cite this article in press as: Carruthers, T., et al., Reprint of “Estimating tag reporting rates for tropical tuna fleets of the Indian Ocean”. Fish. Res. (2014), http://dx.doi.org/10.1016/j.fishres.2014.07.002

G Model FISH-3910; No. of Pages 13

ARTICLE IN PRESS T. Carruthers et al. / Fisheries Research xxx (2014) xxx–xxx

2

estimator based on the concept of Kimura (1976) that operates on data that are disaggregated by time and space. By assuming that the US longline observer programme was reporting all of the tags that were caught, it was possible to inform the reporting rates of commercial fleets fishing Atlantic tunas. In the absence of catch and tagging data stratified by size, the method applied by Carruthers and McAllister (2010) assumed that tags were mixed across size classes. In practice tags are likely to be distributed unevenly throughout the size-structure of a population, therefore limiting the comparability of fleets of differing age-vulnerability schedules. The conventional tagging data and catch data of the Indian Ocean commercial tuna fishery is different from that in the Atlantic in two regards. (1) While the reporting rates of purse seiners are estimated to be high (Hillary et al., 2008), there is no fleet for which it can be said that reporting rate is 100%. (2) Both tag recaptures and catches are reported by size, providing the possibility of accounting for size structure in the population of tagged individuals. We seek to estimate the reporting rates of commercial fleets operating in the Indian Ocean by an extension of the approach of Carruthers and McAllister (2010). In this research we investigate a size-structured model and use tag-seeding data to co-estimate the reporting rate of the EU purse seine fleet (as an alternative to an observer fleet with 100% reporting rate). 2. Materials and methods 2.1. Theory Reporting rates are quantified using the theory described by Kimura (1976): com =

Tcom Cobs obs Tobs Ccom

Tobs Tcom = obs Cobs com Ccom

P(R|obs , S) =

S−1



Robs (1 − obs )

R

S−R

(4)

where S is the number of seeded tags and R is the number of seeded tags that were reported by the EU purse seine fleet. For any strata s, the tags reported by a fleet f can be assumed to be distributed according to the negative binomial distribution: P(T |C, , m) =

 f

s



Cf,s − 1 Tf,s



(f ms )

Tf,s

(1 − (f ms ))

Cf,s −Tf,s

(5)

A strata is a division in time and space for which a population of fish can be assumed to have the same mark rate m. For fleets without seeding data, reporting rates were assigned a relatively uninformative beta(1,1) prior. We also conduct a sensitivity analysis of our results to Jeffreys’ (1946), beta(0.5, 0.5) prior for reporting rates that skews greater prior weight towards the tails of the distribution. In this analysis we prescribe the same beta prior for the mark rate of each strata. We used a Bayesian statistical approach to provide probabilistic estimates of reporting rates that may be used readily as priors in later analyses (a sequential Bayesian approach). Markov Chain Monte Carlo (MCMC) simulation using the Gibbs sampler was undertaken using R 2.14.2 (64bit; R Core and Team, 2012), the package ‘R2WinBUGS’ and WinBUGS 1.4 (Lunn et al., 2000). Two chains of 20 000 iterations were sampled with a ‘burn-in’ of 2000 samples. 2.2. The data under analysis

(2)

and therefore: Tcom = mcom Ccom



(1)

where T is the number of tags, C is the number of fish caught and the subscripts obs and com refer to the data of an observer fleet assumed to have a known reporting rate of obs and a commercial fleet with unknown reporting rate com . This method may be rephrased in terms of mark rate m, (the fraction of fish at liberty that are tagged, defined here as the probability of catching a tag given a fish is caught) in order to inform reporting rates of other fleets that do not overlap in time and space with the observer fleet: m=

the EU purse seine fishery by assuming a binomial probability of reporting a seeded tag:

(3)

Note that where obs is known, for any strata in which Tobs and Cobs are reported, m is informed. Any fleet that reports Tcom and Ccom in the same strata may be assumed to be operating on the same population of marked fish of mark rate m. It follows that these coincidental observations inform the reporting rate of the commercial fleet. If reporting rates can be assumed to be constant over time and space this commercial reporting rate will then serve to inform the reporting rates of other fleets with coincidental data (even if they do not overlap directly with the observer fleet). In this way information regarding commercial reporting rates flows from the observer fleet through a network of mark rates and overlapping tag recovery observations. In this application the observer fleet is the European Union (EU) purse seine fishery (i.e. vessels fishing with French, Spanish and Seychelles flags) for which there are independent tag seeding data with which to estimate reporting rate (see the Section ‘data under analysis’ below). We quantify the probability of reporting a tag in

From 2002 to 2009 the IOTTP tagged 186 318 tropical tuna with conventional tags (Table 1) of which 32% were yellowfin, 51% were skipjack and 17% were bigeye. The RTTP carried out the majority of the tagging (87%) obtaining a somewhat greater recovery rate than the small-scale tagging operations (17.1% and 14.7%, respectively). Recovery rates were generally comparable among the three tuna species at around 17%. In the case of the RTTP, tag release data were recorded on board the tagging vessel in an electronic database. For each tag release and recovery the following information was recorded: tag number, species, fish size, date, time, geo-position (with precision), tag type and tagger. Recovery data were collected either at sea, directly on board the unloading vessels whilst in port or during transhipment from the vessels to the canneries or in canneries during processing. Measures were taken to ensure that most tagged fish (even those recaptured at sea) were detected, identified, measured and weighed by trained technical officers under the supervision of the RTTP. Observer coverage included all of the major ports where purse-seiners unload their catch in addition to the major canneries. For artisanal and longline fisheries, the RTTP worked with national fisheries administrations whose officers were trained by the project. All reported tags were rewarded in cash or in kind. Verification and control procedures were implemented at different levels to ensure the best possible data quality. The database was made available to scientists including both the original data as well as the error-corrected version. The data of the IOTTP are publically available following a request to the IOTC secretariat (IOTC, 2013) (the tag recovery file used in this analysis is dated June 2012). In addition to the RTTP and small-scale tagging programmes described above, from 2004 to 2009 the IOTC conducted a tag seeding experiment onboard the European Purse-Seine fleet based in the Seychelles. Tuna were secretly tagged by fisheries observers

Please cite this article in press as: Carruthers, T., et al., Reprint of “Estimating tag reporting rates for tropical tuna fleets of the Indian Ocean”. Fish. Res. (2014), http://dx.doi.org/10.1016/j.fishres.2014.07.002

G Model

ARTICLE IN PRESS

FISH-3910; No. of Pages 13

T. Carruthers et al. / Fisheries Research xxx (2014) xxx–xxx

3

Table 1 The conventional tagging data of the Indian Ocean Tuna Tagging Project (IOTTP) 2002–2009 comprising the Regional Tuna Tagging Project (RTTP) and Small-Scale tagging operations (SS). Yellowfin (YFT), skipjack (SKJ) and bigeye (BET) tunas were the target of the tagging operations. Both double and single tags were used in this reporting rate estimation. Recovery rate is the percentage of released tags that have been recaptured so far. Releases YFT

Recaptures SKJ

BET

Total

YFT

Recovery rate SKJ

BET

Total

YFT

SKJ

BET

Total

RTTP Single tag Double tag Total % Total

41 761 10 683 52 444 32.5

67 205 9626 76 831 28.4

24 527 7519 32 046 16.6

133 493 27 828 161 321

7579 2069 9648 35.0

10 963 1542 12 505 27.4

4206 1244 5450 16.5

22 748 4855 27 603

18.1 19.4 18.4

16.3 16.0 16.3

17.1 16.5 17.0

17.0 17.4 17.1

SS Single Tag Double Tag Total % Total

6585 323 6908 27.6

17,024 495 17 519 40.7

511 59 570 2.2

24 120 877 24 997

702 62 764 20.7

2749 70 2819 42.7

95 6 101 2.7

3546 138 3684

10.7 19.2 11.1

16.1 14.1 16.1

18.6 10.2 17.7

14.7 15.7 14.7

IOTTP (RTTP + SS) 48,346 Single Tag 11,006 Double Tag 59 352 Total 31.9 % Total

84,229 10,121 94 350 30.1

25,038 7578 32 616 14.9

157 613 28 705 186 318

8281 2131 10 412 33.3

13,712 1612 15 324 29.4

4301 1250 5551 15.1

26 294 4993 31 287

17.1 19.4 17.5

16.3 15.9 16.2

17.2 16.5 17.0

16.7 17.4 16.8

or voluntary skippers before the fish were placed in the brine wells. The seeded tags were comparable to those used in the tagging and release of live fish and were implanted in the same location on the fish, at the base of the second dorsal fin. In this way it may be assumed that the detection rates of the stevedores unloading the boat and the workers processing the fish are comparable to those of the wider RTTP experiment. The only difference among the seeding tags and those released in the RTTP was the material of the barb. Seeded tags were implanted on dead fish and consequently the anchorage of the tag is not secured by the healing of the fish around the attachment. To avoid shedding, metal attachments were used in the seeding experiment. During each trip, 15 tags and one applicator was provided to the tagger who was asked to tag the three species in different wells and to spread the tags among different size categories. Since 2004, 3420 tunas were seeded and 2961 have been reported (86.5%). In this analysis we use recovery data for years after 2005. In years before 2006 substantial temporal changes in reporting rate were observed that would not be consistent with the constant reporting rate assumptions of this analysis (Hillary et al., 2008). The data of the small scale tagging operations was not used in this analysis because these data are considered to be of less consistent quality compared with the RTTP

due to the patchiness of releases and variability of reporting protocols. 2.3. Definitions of fleets for which reporting rates were estimated We define 13 fleets according to the flag and fishing gear type (e.g. Spanish longline) (Table 2). In this study reporting includes the probability of detecting a tag and then recording it correctly. The gear division accounts for significant differences in observation processes. For example detecting tags among many fish simultaneously brought aboard a purse seiner versus single fish in the case of longliners. We chose to divide reporting rates by flag to account for varying data collection standards among nations. In some cases these fleet definitions include multiple flags with one flag contributing the majority of the catch and tag recaptures. For example, under the ‘All countries bait boat’ (ALL BB) fleet, the Maldavian bait boat fishery makes up over 95% of the catches of tropical tuna from 2006 to 2010. A simplistic evaluation (assuming fishing operations and mark rates are homogeneous in time and space) of reported tags per fish indicates substantial differences in the reporting rate among these 13 fleets (Table 3). For example, some longline fleets report around 300 tags per million fish caught (e.g. Spain and South Africa), approximately thirty times higher than the longline fleets of other nations.

Table 2 The disaggregation of fishing operations in the Indian Ocean for which individual reporting rates were estimated. We define 13 ‘fleets’ according to different combinations of flag and gear. In some cases these ‘fleets’ encompass fishing operations of multiple flags or gear types, for example the baitboat operations of all flags is aggregated under ‘All countries–Bait boat’ or ‘ALL BB’. Flag

Gear

Area

Fleet code

Description

All countries All countries All Countries China

Bait boat Gill net Handline Longline

W W W W/E

ALL BB ALL GILL ALL HAND CHN LL

Pole and line baitboat vessels of all countries operating in the Western Indian Ocean Gillnet vessels of all countries operating in the Western Indian Ocean Handline vessels of all countries operating in the Western Indian Ocean Chinese longline vessels operating throughout the Indian Ocean

Spain France Japan Other flags

Longline Longline Longline Longline

W W W/E W/E

ESP LL FRA LL JPN LL OTH LL

Spanish longline vessels operating in the Western Indian Ocean French longline vessels operating in the Western Indian ocean Japanese longline vessels operating throughout the Indian Ocean Longline vessels of other flags operating throughout the Indian Ocean

Chinese Taipei and Seychelles South Africa All countries All countries

Longline

W/E

TWN + SYC LL

Longline vessels of Chinese Taipei and the Seychelles operating throughout the Indian Ocean

Longline Other gears Other gears

W W E

ZAF LL ALL OTH-W ALL OTH-E

Longline vessles of South Africa operating in the Western Indian Ocean All countries of all remaining gears operating in the Western Indian Ocean All countries of all remaining gears operating in the Eastern Indian Ocean

European Union

Purse seine

W/E

EU PS

Purse seine vessels of the European Union (Spain, France and Seychelles) operating throughout the Indian Ocean

Please cite this article in press as: Carruthers, T., et al., Reprint of “Estimating tag reporting rates for tropical tuna fleets of the Indian Ocean”. Fish. Res. (2014), http://dx.doi.org/10.1016/j.fishres.2014.07.002

G Model

ARTICLE IN PRESS

FISH-3910; No. of Pages 13

T. Carruthers et al. / Fisheries Research xxx (2014) xxx–xxx

4

Table 3 The total number of fish caught (millions) and recapture numbers by fleet and gear. The average recapture rate (tags recaptured per million fish is also included). Assuming a single mixed strata, an approximate point estimate of reporting rate can be calculated for non-EU purse seine fleets (‘Simple rep. rate estimate’) by multiplying their recapture rate by the assume reporting rate of the EU purse seine fleet (95%; 2315 tags seeded, 2204 reported since 2006) and dividing this by the recapture rate of the EU purse seine fleet. Flag

Gear

Catch numbers (M)

All countries All countries All Countries China

Bait boat Gill net Handline Longline

203.99 104.04 7.48 0.72

3815 205 160 35

18.7 2.0 21.4 48.5

28.4% 3.0% 32.4% 73.6%

Spain France Japan Other flags

Longline Longline Longline Longline

0.03 0.10 2.60 6.46

7 8 63 67

276.7 77.4 24.2 10.4

419.6% 117.3% 36.7% 15.7%

Chinese Taipei and Seychelles South Africa All countries All countries

Longline Longline Other gears East Other gears West

6.08 0.03 219.91 59.92

125 9 74 281

20.6 340.6 0.3 4.7

31.2% 516.5% 0.5% 7.1%

European Union

Purse seine

415.28

26,016

62.6

95.0%

2.4. The spatio-temporal resolution of comparisons The base case model assumed that mark rates of tunas were disaggregated by species, quarter, area and size. We modelled mark rates for skipjack (K. pelamis), yellowfin (T. albacares) and bigeye (T. obesus) tuna. Within year stratification by quarter are according to season and defined as January–March, April–June, July–September, October–December. The base-case model assumes four discrete areas that are illustrated in Fig. 1.These time and area strata have been chosen in order to be smallest strata that are compatible with the basic IOTC catch-at-size data. The choice of these 4 areas was also conditioned by the observed fishing locations of the various

Number of recaptures

Average recapture rate

Simple rep. rate estimate

fleets and gears proving one central area in which the majority of fishing activities occur (Equatorial West) and three peripheral areas (North West, South West and East). Mark rates were separated into two size categories depending on the species. Catches and recaptures of skipjack tuna were divided in to those below and above 55 cm. Catches and recaptures of yellowfin and bigeye tuna were divided into those below and above 90 cm. The two size categories chosen for yellowfin and bigeye provide a division that broadly separates immature and mature fishes and also accounts for difference in vulnerability at size of the two principal gear types: longline (principally greater than 90 cm) and purse seine (both less than and greater than 90 cm) (Fig. 2,

Fig. 1. Area definitions and the distribution and composition of EU purse seine catch in the Indian Ocean from 2006 to 2010. The area of the pie charts is proportional to catch (maximum size is 4376 tonnes). The insert illustrates the broad geographic area definitions used to define the ‘base case’ and ‘two area’ estimation models. Mark rates are disaggregated by all four areas in the base-case model. The ‘two area’ model divides marked tags into Eastern and Western areas (combining ‘North West’, ‘Equatorial West’ and ‘South West’ areas).

Please cite this article in press as: Carruthers, T., et al., Reprint of “Estimating tag reporting rates for tropical tuna fleets of the Indian Ocean”. Fish. Res. (2014), http://dx.doi.org/10.1016/j.fishres.2014.07.002

G Model FISH-3910; No. of Pages 13

ARTICLE IN PRESS T. Carruthers et al. / Fisheries Research xxx (2014) xxx–xxx

Fig. 2. The length composition of catches by species and gear type, 2006–2010. The vertical dashed line represents the size division for mark rates (90 cm for bigeye and yellowfin, 55 cm for skipjack).

panels a and b). The two size categories chosen for skipjack separate the two modes of the bimodal size frequency distribution found in the Maldivian bait boat fishery (Fig. 2, panel c). For fleets without seeding data reporting rates are assigned a relatively uninformative beta(1,1) prior. The same uninformative prior is prescribed to the mark rate for each strata. An example of a stratum under the base case model would be tags per skipjack tuna in the Eastern Indian Ocean in the period January–March in 2004 for individuals below 55 cm. There is evidence for rapid mixing of tags with average recapture distance rapidly stabilising at around 750 km for all three species after just 30 days (Fig. 3). For this reason the base case estimation made use of all recaptured tags, even those caught soon after release (this assumption was subject to sensitivity analysis). To illustrate the sensitivity of the model outputs to the definition of mark rates we consider three other mark-rate definitions according to a two area model (two area, dividing mark rates into eastern and western Indian Ocean by 80◦ E, Fig. 1), a model that aggregates marked fish to year (no quarter) and the base-case model applied to recapture data for only those tags that have been at liberty for over 90 days (DAL >90). While there is evidence for relatively rapid mixing of tags in the Indian Ocean (Fig. 3) we chose to ignore recaptures before 90 days to evaluate the effect of an alternative mixing scenario on the estimates of reporting rate. The base case model and the three sensitivity cases are described in Table 4, including the number of estimated mark rates and the total number of comparisons (occasions when two fleets report tags and catch in the same strata). A more detailed break-down in the base case-comparisons (Table 5) reveals that all fleets directly overlap with the EU purse seine fleet for which reporting rate is estimated from the tag seeding experiment.

5

chains. According to trace plots of the MCMC chains, Gelman and Rubin (1992) and Geweke (1992) diagnostics, convergence could not be rejected for the base-case and sensitivity models (see Fig. B.1 for convergence plots for the base-case model). After a ‘burn-in’ of 1000 iterations, the posterior estimates were approximated from 20 000 samples. MCMC chain autocorrelation was negligible and mean estimates of all reporting rates varied less than 0.2% given chain thinning up to 1 in every 1, 10 and 50 MCMC samples. For all estimated reporting rates and mark rates, MC error was less than 0.1%. The posterior estimates of reporting rate vary widely among the different fleets (Table 6 and Fig. 4). On the basis of the data from the tag seeding experiment, the reporting rate of the EU purse seine fleet was estimated to be 94%. This estimate was very precise with a standard deviation of just half a percent. All of the other fleets are estimated to report less than 1 in every four tags on average. The longline fleets of the Japan, Chinese Taipei, France and China had among the lowest reporting rates, reporting between 4 and 7 tags for every 100 captured. The estimate for the Spanish longline fleet was among the highest of the commercial fleets, reporting 22 tags in every 100 captured. The precision of reporting rate estimates also varied widely. For example, despite similar mean values the reporting rate for hand line operators (‘ALL HAND’) was estimated with a standard deviation ¼ that of the South African longline fleet (‘ZAF LL’). In general, the estimates of reporting rate were most sensitive to annual aggregation (no quarter) and assuming two areas for the mark rates (two area) (Table 7 and Fig. 5). In the majority of cases aggregating the mark rates lead to a strong inflation in estimated reporting rates. This is particularly the case for the ‘no quarter’ sensitivity analysis where all reporting rates were estimated to be higher than under the base case assumptions, typically ranging from 10 to 100% larger. Reporting rates become inflated in response to lower estimated mark rates; to get the same number of observed tag recaptures, a higher reporting rate is estimated. This indicates that spatial and temporal aggregation leads to lower mean estimates of mark rates and therefore that the EU purse-seine fleet is operating on higher mark rates that are specific to finer spatiotemporal scales. Removing tags caught before 90 days at liberty (DAL >90) led to mostly negative reductions in reporting rate of much smaller magnitude (typically between 0 and 10% reductions although the reporting rate for all baitboat fisheries (All BB) was 85% lower. The sensitivity of the EU reporting rate estimate to different model assumptions may be counter intuitive to some readers since it is the focal fleet from which all other reporting rates are estimated. This sensitivity simply demonstrates that the relatively uninformative beta priors assigned to the other fleets still carry sufficient information to distort EU purse seine estimates under different assumptions about the spatio-temporal aggregation of mark rates. Calculation of the Deviance Information Criterion for each model revealed that the base-case and ‘two area’ models were the most parsimonious explanation of the observed tag and catch data (DIC scores for the ‘base-case’, ‘two area’, ‘no quarter’ and ‘no size’ models were 20 133, 18 839, 32 574 and 32 204, respectively). While the reporting rate estimates were sensitive to structural assumptions of the model (the spatio-temporal resolution of comparisons) they did not change greatly when estimated from Jeffreys’ (1946) beta prior distribution (Table 6).

3. Results

4. Discussion

Posterior estimates of reporting rates were not strongly correlated (Table A.1 and Fig. A.1) leading to rapid mixing of MCMC

At 94% the mean estimate of the reporting rate of the EU purse seine fleet (that had the tag seeding experiment) was very high.

Please cite this article in press as: Carruthers, T., et al., Reprint of “Estimating tag reporting rates for tropical tuna fleets of the Indian Ocean”. Fish. Res. (2014), http://dx.doi.org/10.1016/j.fishres.2014.07.002

G Model

ARTICLE IN PRESS

FISH-3910; No. of Pages 13

T. Carruthers et al. / Fisheries Research xxx (2014) xxx–xxx

6

Fig. 3. The distance between tag recapture and release relative to duration at liberty. The points represent individual tags. Plotted are recaptures of bigeye, yellowfin and skipjack tuna (3605, 5815 and 5786 recaptures, respectively) released from tagging operations off the coast of Tanzania from 2006 to 2010 (approximately 78% of the IOTTC-wide recaptures). The solid black line is the mean distance trend. The solid grey line is the percentage of tags recaptured after a particular duration at liberty. The vertical dashed line denotes 90 days at liberty that was used as a cut-off in the sensitivity analysis.

Table 4 The four models for which mark rates are estimated at different levels of disaggregation. The term ‘quarter’ refers to a quarter of the year (e.g. January-March, April-June). Model name

Disaggregation of mark rates

Number of strata for which mark rate is estimated

Total number of comparisons

Base case 2 area No quarter DAL >90

Year × quarter × 4 areas × size × species Year × quarter × 2 areas × size × species Year × 4 areas × size × species Year × quarter × 4 areas × size × species

573 288 144 573

7504 5958 2918 7504

Estimates for the remaining fleets were much lower and ranged from 26% to less than 2% (except all countries fishing other gears in the eastern Indian Ocean that on average reported less than 1% of tags). There are a number of implications for both stock assessment and future tagging. Integrated stock assessments that seek

to infer fishing mortality rate (and potentially also natural mortality rate) from both the tagging data in addition to catch and effort data should account for differences in fleet specific reporting rates. Assuming that reporting rates are similar among fleets will likely generate disagreement in the inferred fishing mortality rate from

Table 5 The number of coincidental observations of catch and tagging data for the base-case scenario (observations by fleet in the same strata e.g. year × quarter × area × size × species).

ALL BB ALL GILL ALL HAND CHN LL ESP LL FRA LL JPN LL OTH LL TWN + SYC LL ZAF LL ALL OTH-E ALL OTH-W

ALL GILL

ALL HAND

CHN LL

ESP LL

FRA LL

JPN LL

OTH LL

TWN + SYC LL

ZAF LL

ALL OTH-E

ALL OTH-W

EU PS

76

107 158

36 38 58

56 40 60 72

36 20 40 72 80

56 56 76 122 120 80

56 78 98 140 120 80 200

54 72 92 134 116 80 192 224

0 0 0 32 42 40 42 42 42

0 0 0 32 0 0 56 60 58 0

116 160 189 92 120 80 136 161 153 42 0

116 120 149 89 88 58 125 147 138 20 64 228

Please cite this article in press as: Carruthers, T., et al., Reprint of “Estimating tag reporting rates for tropical tuna fleets of the Indian Ocean”. Fish. Res. (2014), http://dx.doi.org/10.1016/j.fishres.2014.07.002

G Model

ARTICLE IN PRESS

FISH-3910; No. of Pages 13

T. Carruthers et al. / Fisheries Research xxx (2014) xxx–xxx

7

Table 6 The posterior probability density estimates of tag reporting rate for the 13 fleets. The column ‘SD’ refers to the standard deviation of the posterior. Mean and standard deviation results are also included for a sensitivity run assuming Jeffreys’ beta(0.5, 0.5) prior for reporting rates. Reporting rate %

Mean

Flag

Gear

SD

Percentiles

beta(0.5, 0.5) prior

5

10

50

90

95

Mean

SD

EU

PS

93.64

0.58

92.65

92.88

93.66

94.37

94.57

93.64

0.58

ALL ALL ZAF

BB HAND LL

25.85 18.78 16.43

0.50 1.60 4.95

25.04 16.27 9.52

25.21 16.77 10.63

25.85 18.73 15.81

26.49 20.86 23.01

26.66 21.48 25.48

25.85 18.71 15.24

0.50 1.60 4.63

ESP ALL CHN

LL GILL LL

12.69 12.02 7.25

4.60 0.88 1.27

6.34 10.61 5.30

7.35 10.91 5.69

12.05 12.00 7.19

18.85 13.17 8.92

21.25 13.51 9.41

0.00 0.00 7.06

0.00 0.00 1.25

JPN FRA ALL

LL LL OTH-W

4.22 3.77 3.62

0.56 1.38 0.25

3.35 1.87 3.22

3.53 2.18 3.31

4.19 3.59 3.61

4.95 5.59 3.95

5.21 6.28 4.04

4.12 0.00 0.00

0.54 0.00 0.00

TWN + SYC OTH ALL

LL LL OTH-E

3.49 1.94 0.01

0.38 0.31 0.00

2.88 1.47 0.00

3.01 1.56 0.01

3.47 1.92 0.01

4.00 2.34 0.01

4.14 2.47 0.01

3.42 1.87 0.01

0.37 0.29 0.00

Fig. 4. Posterior probability density plots for the estimated reporting rates. The black point on each line represents the mean estimate of reporting rate. The most central range depicted by a solid black line is the 50% probability interval. The next most central range is the 90% probability interval and is represented by a black dashed line. Finally the 95% and 99% probability intervals are represented by grey lines that are solid and dashed, respectively.

different data sources that may lead to biases in the estimation of key reference points such as current stock depletion and fishing mortality rate. Reporting rates may also strongly affect inferences about movement and stock mixing. For example, it is likely that correctly accounting for the relatively low reporting rates of the eastern Indian Ocean tuna fleets will increase the inferred rate of

stock mixing since the majority of tags were released in the western Indian Ocean. The reporting rate estimates of this study were considerably higher than those of the same flags and gears fishing in the Atlantic Ocean (Carruthers and McAllister, 2010). For example in this analysis the Japanese, French and Spanish longline fleets are estimated

Table 7 The sensitivity of posterior estimates of reporting rate to assumptions regarding spatio-temporal stratification and the inclusion of size classes. The ‘base case’ scenario includes stratification by year, quarter (e.g. January–March), size (small/large), area (eastern/3 western areas) and species (bigeye, yellowfin or skipjack). The alternative versions ‘two area’, ‘no quarter’ and ‘DAL >90’ are the results from three models that assume eastern and western stratification, do not stratify mark rates by quarter and ignore tags caught before 90 days at liberty, respectively. Reporting rate %

Mean

SD

Flag

Gear

Base case

Two area

No quarter

DAL >90

Base case

Two area

No quarter

DAL >90

EU ALL ESP ZAF

PS BB LL LL

93.64 25.85 12.69 16.43

94.52 27.25 56.96 61.89

94.86 29.52 54.45 54.07

93.64 4.02 12.38 16.09

0.58 0.50 4.60 4.95

0.50 0.52 17.19 14.60

0.47 0.55 18.03 15.58

0.58 0.18 4.59 4.84

ALL CHN ALL FRA

HAND LL GILL LL

18.78 7.25 12.02 3.77

9.71 8.91 6.04 10.19

23.28 11.90 15.07 12.93

22.24 7.21 11.01 3.77

1.60 1.27 0.88 1.38

0.74 1.53 0.41 3.42

1.86 2.03 1.05 4.70

1.84 1.28 0.86 1.40

ALL JPN TWN + SYC OTH

OTH-W LL LL LL

3.62 4.22 3.49 1.94

2.66 5.67 4.37 2.35

6.05 8.05 7.18 8.23

3.32 4.14 3.36 1.84

0.25 0.56 0.38 0.31

0.16 0.69 0.44 0.36

0.37 0.97 0.69 1.06

0.26 0.55 0.37 0.29

ALL

OTH-E

0.01

0.01

0.30

0.01

0.00

0.00

0.06

0.00

Please cite this article in press as: Carruthers, T., et al., Reprint of “Estimating tag reporting rates for tropical tuna fleets of the Indian Ocean”. Fish. Res. (2014), http://dx.doi.org/10.1016/j.fishres.2014.07.002

G Model FISH-3910; No. of Pages 13 8

ARTICLE IN PRESS T. Carruthers et al. / Fisheries Research xxx (2014) xxx–xxx

Fig. 5. The sensitivity of posterior estimates of reporting rate to assumptions regarding spatio-temporal stratification and the inclusion of size classes. The ‘base case’ scenario includes stratification by year, quarter (e.g. spring), size (small/large), area (eastern/western Indian Ocean) and species (bigeye, yellowfin or skipjack). The alternative versions ‘two area’, ‘no quarter’ and ‘DAL >90’ are the results from three models that assume eastern and western stratification, do not stratify mark rates by quarter and ignore tags caught before 90 days at liberty, respectively.

to have mean reporting rates of 4.2, 5.0 and 21.9 percent compared with 0.09, 0.13 and 0.11 percent in the case of the Atlantic study. This difference may be explained by the disparity in the recovery schemes that were implemented in the Atlantic and Indian Oceans.

While most of the Atlantic tag recovery schemes are administered and reported by individual nations, the Indian Ocean programme was a coordinated multi-nationally with a unified publicity campaign and a centralised system of recording tags. Scale may also be

Please cite this article in press as: Carruthers, T., et al., Reprint of “Estimating tag reporting rates for tropical tuna fleets of the Indian Ocean”. Fish. Res. (2014), http://dx.doi.org/10.1016/j.fishres.2014.07.002

G Model FISH-3910; No. of Pages 13

ARTICLE IN PRESS T. Carruthers et al. / Fisheries Research xxx (2014) xxx–xxx

a contributing factor since Atlantic tuna populations are exploited by many more nations over a larger spatial scale that encompasses a wider range of international relationships and regional interests. A central opportunity of the IOTTP was the collection of more detailed data than that of previous pelagic tagging programmes. Probably the most important area of improvement was the collection of additional size data that allows for explicit modelling of mark-rates by size class and therefore the ability to account for broad differences in the size selectivity of different fishing gears (e.g. small yellowfin and bigeye are caught in large numbers by purse seiners but are seldom caught by longliners). Hearn et al. (1999) identify the potential biases when aggregating tag recaptures and catch over age groups. A separate sensitivity evaluation of our method indicated a very high sensitivity of the model estimates of reporting rate to aggregation of size classes suggesting that caution should be taken in the interpretation of the reporting rates of Carruthers and McAllister (2010). The coarse area definitions of this analysis ensured that all fleets had observations that overlapped directly with the EU purse seine fleet for which reporting rate was estimated from the tag seeding experiment. This is quite different from the Atlantic analysis of Carruthers and McAllister (2010) that attempted a similar approach but on a much finer spatial scale for a much larger number of fleets operating over different spatial ranges. Consequently, several of the Atlantic reporting rates were informed indirectly from other commercial fleets rather than directly from the ‘observer’ fleet. In this study, the DIC model selection criterion indicates that even the coarse spatial structure of the four area model might be unnecessary compared with a more simple two area (East and West) model. It should be noted that the method applied here relies on a number of assumptions: (1) tags are distributed homogenously over the spatial and temporal scale of comparisons among fleets (i.e. at the resolution of the estimated mark rates); (2) reporting rates remain constant over time, among species and are the same in areas beyond spatio-temporal comparisons; (3) catches are accurately reported. All of these assumptions are likely to be invalid to some extent. The most important assumption of the method we apply is probably that of spatial homogeneity in tag densities. It is likely that purse-seine catches (Fig. 1) are not distributed in proportion to tuna density throughout the Indian Ocean. It follows that these tagging operations cannot be expected to generate homogeneous mark rates among the four discrete areas of this study. For example the Equatorial West area encompasses both the Tanzanian coast and the Maldives despite a much higher density of tags in the latter region. Similarly, the Eastern area includes a western edge off Sri Lanka (80◦ E) that is likely to include a much higher density of tags than the eastern edge off Indonesia. If the fishing fleets are mixed over this area, the only likely outcome is greater uncertainty in reporting rate estimates. However systematic differences in the distribution of fleets within these areas will lead to biases in reporting rates (e.g. overestimating reporting rates where a fleet operates in a sub-area with relatively high mark rates). When undertaking these analyses relatively large spatial areas were chosen for two reasons: to ensure that catches and recoveries could be reliability assigned to region and in order to maximise the number of instances where fleets overlapped with the EU purse seine fleet (for which there was a tag seeding experiment). For certain fisheries this assumption may be relatively large. For example, the Maldavian bait boat fishery (included in the ‘All BB’ fleet category) has been independently estimated to report at least 70% of tags (S. Adam, personal communication), a rate much higher than that estimated in this analysis (approximately 25%). This suggests that the fishing area of the Maldives contain a localised and distinct population of tropical tunas that do not fully mix with the higher tag densities of the wider Equatorial West region in which it

9

is assigned in this analysis. The result is a serious underestimation of reporting rates for this fleet. An area for future investigation is applying these analyses to those tags and catch with precise spatial information to evaluate in the importance of fine-scale heterogeneity in mark rates (for example vessel specific catch and recapture information). Since all three species of this study exhibit strong shoaling behaviour it is possible that the probability of recapturing two different tags is not independent. The assumption of independence is fundamental to the negative binomial observation model used in this analysis. In this case non-independence would lead to a greater level of variance in observations than assumed by the model, a condition known as ‘overdispersion’. The most likely product of overdispersion in this case is the compression of uncertainty in reporting rate estimates. Consequently, while the reporting rates estimated here may be accurate, we recommend that readers consider the precision of these estimates to be at the upper end of the credible range. It is difficult to assess the significance of the assumption of spatio-temporal homogeneity in reporting rates. Theoretically it would not be difficult to estimate annual reporting rates using the method applied here. However assuming temporally constant reporting rates provided a much greater number of coincidental comparisons among fleets and enabled the estimation of reporting rates for fleets such as South African longliners. There are reasons to expect changes in reporting rate over time for example in response to changes in data-collection practices, management methods, and increasing experience with tagging programmes. For example, Hillary et al. (2008) found evidence that the reporting rate of the EU purse seine fleet increased from 2004 to 2007 and hypothesized that this may be due to an extensive publicity campaign in 2005 to inform fishers of the benefits of the tagging programme. It should be noted that the catch-at-size data used in this analysis were either reported by national scientists or were estimated by the IOTC secretariat. It follows that the catch-at-size data are not the product of a standardized method and were collected and processed according to different protocols for each flag and gear type. Catch-at-size data are generally calculated by uprating a size sample by total catches. Due to small sample sizes there is large uncertainty in the catch-at-size data for most longline fleets. This is also applies to the catch-at-size of artisanal fleets where there is considerable additional uncertainty over the magnitude and location of total catches. It is not clear how these uncertainties in the size data might affect the final reporting rates but future reporting rate estimation could attempt to examine this sensitivity by simulating data subject to a range of biases in the observation processes. Another important limitation of the tagging data relates to observation error in the tag recovery data. To underline the importance of this issue, consider that a substantial fraction of tag recaptures record a different species to that recorded at release. In these instances it was reasonable to assume that the technical officers who tagged the fish identified the species correctly. However, while species reporting may be easy to correct for, there are likely to be other serious inaccuracies in the recovery data that could affect the estimates of this study, for example, location, time and size of recaptures. To a limited extent it may be possible to account for these uncertainties in further mark-recapture analyses by evaluating the sensitivity of key quantities (abundance, exploitation rate, mixing rate) to the reporting rates estimated in our various sensitivity analyses. Total tag recovery rates were approximately 15% across all fleets. This rate may be improved in future large-scale tagging programmes by more extensive observer coverage on board large longline vessels and at the locations of significant tuna landings (ports, beaches). While the cost of a conventional spaghetti tag may be low, there are considerable deployment costs. A 15% recapture

Please cite this article in press as: Carruthers, T., et al., Reprint of “Estimating tag reporting rates for tropical tuna fleets of the Indian Ocean”. Fish. Res. (2014), http://dx.doi.org/10.1016/j.fishres.2014.07.002

G Model FISH-3910; No. of Pages 13 10

ARTICLE IN PRESS T. Carruthers et al. / Fisheries Research xxx (2014) xxx–xxx

rate may be sufficiently low to justify the use of more expensive tag technologies in future tagging studies. For example if the objective is gaining an understanding of migration and stock mixing, pop-off satellite archival tags have become significantly cheaper in recent years (approximately US$100 per tag) and do not rely on human reporting. Alternatively, if fishing mortality rate estimation was the priority, passive integrated transponder technology (PIT tags) or gene tagging (Buckworth et al., 2012) offer alternative solutions that are less dependent on human reporting.

this publication were collected under the Indian Ocean Tuna Tagging Programme comprising the Regional Tuna Tagging Project of the Indian Ocean funded under the 9th European Development Fund (9.ACP.RSA.005/006) of the European Union, and several small-scale tagging projects funded by the European Union, the Government of Japan and the People’s Republic of China. We wish to acknowledge the contributions of all the people that have been involved in the Indian Ocean Tuna Tagging Programme. Many additional thanks to Viveca Nordstrom for preparing the data for these analyses.

Acknowledgements TRC is grateful for the support of Lenfest Ocean Programme of the Pew Charitable Trusts. The tuna tagging data analysed in

Appendix A. Posterior cross correlation of reporting rates

Fig. A.1. The posterior correlation plots for each reporting rate estimate (logit transformed) of the base-case model. Plotted are 1000 samples (the full chain of 20 000 ‘thinned’ at a rate of 1 in.

Please cite this article in press as: Carruthers, T., et al., Reprint of “Estimating tag reporting rates for tropical tuna fleets of the Indian Ocean”. Fish. Res. (2014), http://dx.doi.org/10.1016/j.fishres.2014.07.002

ALL HAND

CHN LL

ESP LL

FRA LL

JPN LL

OTH LL

TWN + SYC LL

ZAF LL

ALL OTH-E

ALL OTH-W

EU PS

−1.05405 0.00067

−1.99295 0.00013 0.00691

−1.46763 0.00010 0.00084 0.01101

−2.56343 0.00011 0.00025 0.00041 0.03596

−1.99298 0.00012 0.00011 0.00051 0.00585 0.17664

−3.30525 0.00009 0.00048 0.00035 0.00370 0.02160 0.14746

−3.13045 0.00003 0.00011 0.00020 0.00272 0.00831 0.00696 0.01919

−3.93659 0.00004 0.00016 0.00052 0.00293 0.00659 0.00650 0.00398 0.02584

−3.32556 0.00007 0.00011 0.00050 0.00331 0.00725 0.00707 0.00361 0.00527 0.01298

−1.66912 0.00013 0.00008 0.00047 0.00519 0.02539 0.02221 0.00910 0.00800 0.00855 0.12916

−9.59321 −0.00004 −0.00001 0.00070 0.00208 0.00324 0.00328 0.00235 0.01458 0.00392 0.00398 0.05760

−3.28449 0.00009 0.00064 0.00036 0.00030 0.00095 0.00044 0.00031 0.00028 0.00031 0.00042 0.00023 0.00509

2.69364 0.00081 0.00053 0.00060 0.00068 0.00097 0.00103 0.00056 0.00054 0.00061 0.00119 0.00039 0.00061 0.00957

ARTICLE IN PRESS

ALL GILL

G Model

FISH-3910; No. of Pages 13

Mean ALL BB ALL GILL ALL HAND CHN LL ESP LL FRA LL JPN LL OTH LL TWN + SYC LL ZAF LL ALL OTH-E ALL OTH-W EU PS

ALL BB

T. Carruthers et al. / Fisheries Research xxx (2014) xxx–xxx 11

Please cite this article in press as: Carruthers, T., et al., Reprint of “Estimating tag reporting rates for tropical tuna fleets of the Indian Ocean”. Fish. Res. (2014), http://dx.doi.org/10.1016/j.fishres.2014.07.002

Table A.1 The posterior correlation among estimated reporting rates of the base-case model. The rates are logit-transformed to allow any correlation structure to be approximated by a multivariate normal distribution.

G Model FISH-3910; No. of Pages 13

ARTICLE IN PRESS T. Carruthers et al. / Fisheries Research xxx (2014) xxx–xxx

12

Appendix B. MCMC convergence 20

Fig. B.1. The progression of two MCMC chains (thinned to one in every 10 samples) for each reporting rate estimate of the base case model.

References Buckworth, R.C., Ovenden, J.R., Broderick, D., Macbeth, G.M., McPherson, G.R., Phelan, M.J., 2012. GENETAG: Genetic Mark-recapture for Real-time Harvest Rate Monitoring (Pilot Studies in Northern Australia Spanish mackerel fisheries). Fisheries Report No. 107. Northern Territory Government, Australia http://www.nt.gov.au/d/Content/File/p/Fish Rep/FR107.pdf Carruthers, T.R., McAllister, M., 2010. Estimating reporting rates using coincidental tag recaptures. Aquat. Living Resour. 23, 343–352. Gelman, A., Rubin, D.B., 1992. Inference from iterative simulation using multiple sequences. Stat. Sci. 7, 457–472.

Geweke, J., 1992. Evaluating the accuracy of sampling-based approaches to calculating posterior moments. In: Bernardo, J.M., Berger, J.O., Dawid, A.P., Smith, A.F.M. (Eds.), Bayesian Statistics 4. Clarendon Press, Oxford, UK. Hallier, J.P., Million, J., 2009. The Contribution of the Regional Tuna Tagging Project – Indian Ocean to IOTC Stock Assessment. Working Paper of the Indian Ocean Tuna Commission. IOTC-2009-WPTT-24. Hearn, W.S., Polacheck, T., Pollock, K.H., Whitelaw, W., 1999. Estimation of tag reporting rates in age-structured multicomponent fisheries where one component has observers. Can. J. Fish. Aquat. Sci. 56, 1255–1265. Hillary, R.M., Million, J., Anganuzzi, A., Areso, J.J., 2008. Tag Shedding and Reporting Rate Estimates for Indian Ocean Tuna Using Double-Tagging and Tag-seeding

Please cite this article in press as: Carruthers, T., et al., Reprint of “Estimating tag reporting rates for tropical tuna fleets of the Indian Ocean”. Fish. Res. (2014), http://dx.doi.org/10.1016/j.fishres.2014.07.002

G Model FISH-3910; No. of Pages 13

ARTICLE IN PRESS T. Carruthers et al. / Fisheries Research xxx (2014) xxx–xxx

Experiments. Working Paper of the Indian Ocean Tuna Commission. IOTC-2008http://www.iotc.org/files/proceedings/2008/wptda/IOTC-2008WPTDA-04. WPTDA-04.pdf IOTC, 2013. Indian Ocean Tuna Commission online database. http://www.iotc.org/ English/data/databases.php Jeffreys, H., 1946. An invariant form of the prior probability in estimation problems. Proc. R. Soc. A 186 (1007), 53–461. Kimura, D.K., 1976. Estimating the total number of marked fish present in a catch. Trans. Am. Fish. Soc. 105, 664–668. Lunn, D.J., Thomas, A., Best, N., Spiegelhalter, D., 2000. WinBUGS – a Bayesian modelling framework: concepts, structure, and extensibility. Stat. Comput. 10, 325–337.

13

Pollock, K.H., Hoenig, J.M., Hearn, W.S., Calingert, B., 2001. Tag reporting rate estimation: 1 an evaluation of the high-reward tagging method. N. Am. J. Fish. Manage. 21, 521–532. Pollock, K.H., Hearn, W.S., Polacheck, T., 2002. A general model for tagging on multiple component fisheries: an integration of age-dependent reporting rates and mortality estimation. Environ. Ecol. Stat. 9, 57–69. R Core Team, 2012. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria http://www.R-project. org

Please cite this article in press as: Carruthers, T., et al., Reprint of “Estimating tag reporting rates for tropical tuna fleets of the Indian Ocean”. Fish. Res. (2014), http://dx.doi.org/10.1016/j.fishres.2014.07.002