Observatory (Ob7; https://www.ob7.ird.fr/en/) using the fol-
lowing e-mail address: **adm-db1p@ird.fr**.

Code for carrying out all analyses is available in open access
at the following address: https://github.com/Agathedumont/
modeling-bycatch-abundance-delta-method.

References

Amandè MJ, Ariz J, Chassot E *et al.* Bycatch of the European purse seine tuna fishery in the Atlantic Ocean for the 2003–2007 period. *Aquat Living Resour* 2010;23:353–62.

Andersen MM. Prediction intervals for Generalized Additive Models (GAMs). 2022. https://mikl.dk/post/2019-prediction-intervals-for-gam/ (23 March 2024, date last accessed).

Arrizabalaga H, Dufour F, Kell L *et al.* Global habitat preferences of commercially valuable tuna. *Deep Sea Res II Topic Stud Oceanogr* 2015;113:102–12.

Bell JD, Sharp MK, Havice E *et al.* Realising the food security benefits of canned fish for Pacific Island countries. *Mar Policy* 2019;100:183–91.

Berrar D. Cross-validation. In: Reference Module in Life Sciences. Amsterdam: Elsevier, 2018.

Breiman L. Random forests. *Mach Learn* 2001;45:5–32.

Davies T, Mees C, Milner-Gulland E. The past, present and future use of drifting fish aggregating devices (FADs) in the Indian Ocean. *Mar Policy* 2014;45:163–70.

Dulvy NK, Fowler SL, Musick JA *et al.* Extinction risk and conservation of the world's sharks and rays. *eLife* 2014;3:e00590. https://doi.org/10.7554/eLife.00590

Dunn DC, Maxwell SM, Boustany AM *et al.* Dynamic ocean management increases the efficiency and efficacy of fisheries management. *Proc Natl Acad Sci* 2015;113:668–73. https://doi.org/doi/10.1073/pnas.1513626113

FAO. Report of the expert meeting to develop technical guidelines to reduce bycatch of marine mammals in capture fisheries. Rome: FAO, 2020. http://www.fao.org/documents/card/en/c/ca7620en (6 September 2022, date last accessed).

Fletcher D. Confidence intervals for the mean of the delta-lognormal distribution. *Environ Ecol Stat* 2008;15:175–89.

Floch L, Marsac F, Fily T *et al.* Statistics of the French purse seine fishing fleet targeting tropical tuna in the Indian Ocean (1981–2020). IOTC-2021-WPDCS17-21. Cape Town: Indian Ocean Tuna Commission Working Party on Data Collection (WPDCS), 2021. https://www.iotc.org/WPDCS/17/21 (22 November 2021, date last accessed).

Forget FG, Capello M, Filmalter JD *et al.* Behaviour and vulnerability of target and non-target species at drifting fish aggregating devices (FADs) in the tropical tuna purse seine fishery determined by acoustic telemetry. *Can J Fish Aquat Sci* 2015;72:1398–405. https://doi.org/10.1139/cjfas-2014-0458

Genuer R, Poggi JM, Tuleau-Malot C. VSURF: an R package for variable selection using random forests. R J 2015;7:19.

Genuer R, Poggi JM, Tuleau-Malot C. VSURF: variable selection using random forests. 2022. https://github.com/robingenuer/VSU RF (27March 2024, date last accessed)

Goujon M, Maufroy A, Ra RS *et al.* Collecting data on board French tropical tuna purse seiners with common observers: results of Orthongel's voluntary observer program OCUP in the Atlantic Ocean (2013–2017). *Collect Vol Sci Pap ICCAT* 2017;74:3784–805.

Gräler B, Pebesma E, Heuvelink G. Spatio-temporal interpolation using gstat. R J 2016;8:204–18.

Gregorutti B, Michel B, Saint-Pierre P. Correlation and variable importance in random forests. *Stat Comput* 2017;27:659–78. https://doi.org/10.1007/s11222-016-9646-1

Hutchinson MR, Itano DG, Muir JA *et al.* Post-release survival of juvenile silky sharks captured in a tropical tuna purse seine fishery. *Mar Ecol Prog Ser* 2015;521:143–54. https://doi.org/10.3354/meps11073

Kaplan DM, Chassot E, Amandé JM *et al.* Spatial management of Indian Ocean tropical tuna fisheries: potential and perspectives. *ICES J Mar Sci J du Conseil* 2014; **71**: 1728–49.

Kaplan DM, Tolotti MT. Silky shark abundance index based on CPUE standardization of French Indian Ocean tropical tuna purse seine observer bycatch data. IOTC-2023-WPEB19-34_Rev1. Réunion: IOTC 19th Working Party on Ecosystems and Bycatch, 2023.

Kitagawa T, Nakata H, Kimura S *et al.* Effect of ambient temperature on the vertical distribution and movement of Pacific bluefin tuna *Thunnus thynnus* orientalis. *Mar Ecol Prog Ser* 2000;206:251–60.

Legendre P, Legendre L. *Numerical Ecology*. Amsterdam: Elsevier, 2012.

Lehodey P, Murtugudde R, Senina I. Bridging the gap from ocean models to population dynamics of large marine predators: a model of mid-trophic functional groups. *Prog Oceanogr* 2010;84:69–84.

Liaw A, Wiener M. Classification and regression by randomforest. R News 2002;2:18–22.

Mannocci L, Forget F, Tolotti MT *et al.* Predicting bycatch hotspots in tropical tuna purse seine fisheries at the basin scale. *Glob Ecol Conserv* 2020;24:e01393.

Maufroy A, Kaplan D, Bez N *et al.* Massive increase in the use of drifting fish aggregating devices (dFADs) by tropical tuna purse seine fisheries in the Atlantic and Indian Oceans. *ICES J Mar Sci J du Conseil* 2016;74:fsw175. https://doi.org/10.1093/icesjms/fsw175

Mondal S, Lan YC, Lee MA *et al.* Detecting the feeding habitat zone of albacore tuna (*Thunnus alalunga*) in the southern Indian Ocean using multisatellite remote sensing data. *J Mar Sci Technol* 2022;29:794–807.

Murtaugh PA. In defense of *P* values. *Ecology* 2014;95:611–17.

Onandia I, Grande M, Galaz JM *et al.* New assessment on accidentally captured silky shark post-release survival in the Indian Ocean tuna purse seine fishery. IOTC-2021-WPEB17 (DP)-13. Cape Town: IOTC Working Party on Ecosystems & Biodiversity, 2021.

Ortiz M, Arocha F. Alternative error distribution models for standardization of catch rates of non-target species from a pelagic longline fishery: billfish species in the Venezuelan tuna longline fishery. *Fish Res* 2004;70:275–97. https://doi.org/10.1016/j.fishres.2004.08.028

Pacoureau N, Rigby CL, Kyne PM *et al.* Half a century of global decline in oceanic sharks and rays. *Nature* 2021;589:567–71.

Paiva VH, Geraldes P, Ramirez I *et al.* Overcoming difficult times: the behavioural resilience of a marine predator when facing environmental stochasticity. *Mar Ecol Prog Ser* 2013;486:277–88.

Pianet R, Pallares P, Petit C. New sampling and data processing strategy for estimating the composition of catches by species and sizes in the european purse seine tropical tuna fisheries. 2000. https://aquadocs.org/handle/1834/971 (10 February 2023, date last accessed).

Pons M, Kaplan DM, Moreno G *et al.* Benefits, concerns, and solutions of fishing for tunas with drifting fish aggregation devices. *Fish Fish* 2023;24:979–1002.

Pons M, Watson JT, Ovando D *et al.* Trade-offs between bycatch and target catches in static versus dynamic fishery closures. *Proc Natl Acad Sci* 2022;119:e2114508119. https://doi.org/10.1073/pnas.2114508119

R Core: R: a language and environment for statistical computing. Vignna: R Foundation for Statistical Computing, 2023. https://www.R-project.org/

Ribeiro PJ, Diggle P, Christensen O *et al.* geoR: analysis of geostatistical data. 2023. http://www.leg.ufpr.br/geoR/ (27 March 2024, date last accessed)

Ruiz J, Abascal FJ, Bach P, *et al.* Bycatch of the European, and associated flag, purse-seine tuna fishery in the Indian Ocean for the period
Observatory (Ob7; https://www.ob7.ird.fr/en/) using the fol-
lowing e-mail address: **adm-db1p@ird.fr**.

Code for carrying out all analyses is available in open access
at the following address: https://github.com/Agathedumont/
modeling-bycatch-abundance-delta-method.

References

Amandè MJ, Ariz J, Chassot E *et al.* Bycatch of the European purse seine tuna fishery in the Atlantic Ocean for the 2003–2007 period. *Aquat Living Resour* 2010;23:353–62.

Andersen MM. Prediction intervals for Generalized Additive Models (GAMs). 2022. https://mikl.dk/post/2019-prediction-intervals-for-gam/ (23 March 2024, date last accessed).

Arrizabalaga H, Dufour F, Kell L *et al.* Global habitat preferences of commercially valuable tuna. *Deep Sea Res II Topic Stud Oceanogr* 2015;113:102–12.

Bell JD, Sharp MK, Havice E *et al.* Realising the food security benefits of canned fish for Pacific Island countries. *Mar Policy* 2019;100:183–91.

Berrar D. Cross-validation. In: Reference Module in Life Sciences. Amsterdam: Elsevier, 2018.

Breiman L. Random forests. *Mach Learn* 2001;45:5–32.

Davies T, Mees C, Milner-Gulland E. The past, present and future use of drifting fish aggregating devices (FADs) in the Indian Ocean. *Mar Policy* 2014;45:163–70.

Dulvy NK, Fowler SL, Musick JA *et al.* Extinction risk and conservation of the world's sharks and rays. *eLife* 2014;3:e00590. https://doi.org/10.7554/eLife.00590

Dunn DC, Maxwell SM, Boustany AM *et al.* Dynamic ocean management increases the efficiency and efficacy of fisheries management. *Proc Natl Acad Sci* 2015;113:668–73. https://doi.org/doi/10.1073/pnas.1513626113

FAO. Report of the expert meeting to develop technical guidelines to reduce bycatch of marine mammals in capture fisheries. Rome: FAO, 2020. http://www.fao.org/documents/card/en/c/ca7620en (6 September 2022, date last accessed).

Fletcher D. Confidence intervals for the mean of the delta-lognormal distribution. *Environ Ecol Stat* 2008;15:175–89.

Floch L, Marsac F, Fily T *et al.* Statistics of the French purse seine fishing fleet targeting tropical tuna in the Indian Ocean (1981–2020). IOTC-2021-WPDCS17-21. Cape Town: Indian Ocean Tuna Commission Working Party on Data Collection (WPDCS), 2021. https://www.iotc.org/WPDCS/17/21 (22 November 2021, date last accessed).

Forget FG, Capello M, Filmalter JD *et al.* Behaviour and vulnerability of target and non-target species at drifting fish aggregating devices (FADs) in the tropical tuna purse seine fishery determined by acoustic telemetry. *Can J Fish Aquat Sci* 2015;72:1398–405. https://doi.org/10.1139/cjfas-2014-0458

Genuer R, Poggi JM, Tuleau-Malot C. VSURF: an R package for variable selection using random forests. R J 2015;7:19.

Genuer R, Poggi JM, Tuleau-Malot C. VSURF: variable selection using random forests. 2022. https://github.com/robingenuer/VSU RF (27March 2024, date last accessed)

Goujon M, Maufroy A, Ra RS *et al.* Collecting data on board French tropical tuna purse seiners with common observers: results of Orthongel's voluntary observer program OCUP in the Atlantic Ocean (2013–2017). *Collect Vol Sci Pap ICCAT* 2017;74:3784–805.

Gräler B, Pebesma E, Heuvelink G. Spatio-temporal interpolation using gstat. R J 2016;8:204–18.

Gregorutti B, Michel B, Saint-Pierre P. Correlation and variable importance in random forests. *Stat Comput* 2017;27:659–78. https://doi.org/10.1007/s11222-016-9646-1

Hutchinson MR, Itano DG, Muir JA *et al.* Post-release survival of juvenile silky sharks captured in a tropical tuna purse seine fishery. *Mar Ecol Prog Ser* 2015;521:143–54. https://doi.org/10.3354/meps11073

Kaplan DM, Chassot E, Amandé JM *et al.* Spatial management of Indian Ocean tropical tuna fisheries: potential and perspectives. *ICES J Mar Sci J du Conseil* 2014; **71**: 1728–49.

Kaplan DM, Tolotti MT. Silky shark abundance index based on CPUE standardization of French Indian Ocean tropical tuna purse seine observer bycatch data. IOTC-2023-WPEB19-34_Rev1. Réunion: IOTC 19th Working Party on Ecosystems and Bycatch, 2023.

Kitagawa T, Nakata H, Kimura S *et al.* Effect of ambient temperature on the vertical distribution and movement of Pacific bluefin tuna *Thunnus thynnus* orientalis. *Mar Ecol Prog Ser* 2000;206:251–60.

Legendre P, Legendre L. *Numerical Ecology*. Amsterdam: Elsevier, 2012.

Lehodey P, Murtugudde R, Senina I. Bridging the gap from ocean models to population dynamics of large marine predators: a model of mid-trophic functional groups. *Prog Oceanogr* 2010;84:69–84.

Liaw A, Wiener M. Classification and regression by randomforest. R News 2002;2:18–22.

Mannocci L, Forget F, Tolotti MT *et al.* Predicting bycatch hotspots in tropical tuna purse seine fisheries at the basin scale. *Glob Ecol Conserv* 2020;24:e01393.

Maufroy A, Kaplan D, Bez N *et al.* Massive increase in the use of drifting fish aggregating devices (dFADs) by tropical tuna purse seine fisheries in the Atlantic and Indian Oceans. *ICES J Mar Sci J du Conseil* 2016;74:fsw175. https://doi.org/10.1093/icesjms/fsw175

Mondal S, Lan YC, Lee MA *et al.* Detecting the feeding habitat zone of albacore tuna (*Thunnus alalunga*) in the southern Indian Ocean using multisatellite remote sensing data. *J Mar Sci Technol* 2022;29:794–807.

Murtaugh PA. In defense of *P* values. *Ecology* 2014;95:611–17.

Onandia I, Grande M, Galaz JM *et al.* New assessment on accidentally captured silky shark post-release survival in the Indian Ocean tuna purse seine fishery. IOTC-2021-WPEB17 (DP)-13. Cape Town: IOTC Working Party on Ecosystems & Biodiversity, 2021.

Ortiz M, Arocha F. Alternative error distribution models for standardization of catch rates of non-target species from a pelagic longline fishery: billfish species in the Venezuelan tuna longline fishery. *Fish Res* 2004;70:275–97. https://doi.org/10.1016/j.fishres.2004.08.028

Pacoureau N, Rigby CL, Kyne PM *et al.* Half a century of global decline in oceanic sharks and rays. *Nature* 2021;589:567–71.

Paiva VH, Geraldes P, Ramirez I *et al.* Overcoming difficult times: the behavioural resilience of a marine predator when facing environmental stochasticity. *Mar Ecol Prog Ser* 2013;486:277–88.

Pianet R, Pallares P, Petit C. New sampling and data processing strategy for estimating the composition of catches by species and sizes in the european purse seine tropical tuna fisheries. 2000. https://aquadocs.org/handle/1834/971 (10 February 2023, date last accessed).

Pons M, Kaplan DM, Moreno G *et al.* Benefits, concerns, and solutions of fishing for tunas with drifting fish aggregation devices. *Fish Fish* 2023;24:979–1002.

Pons M, Watson JT, Ovando D *et al.* Trade-offs between bycatch and target catches in static versus dynamic fishery closures. *Proc Natl Acad Sci* 2022;119:e2114508119. https://doi.org/10.1073/pnas.2114508119

R Core: R: a language and environment for statistical computing. Vignna: R Foundation for Statistical Computing, 2023. https://www.R-project.org/

Ribeiro PJ, Diggle P, Christensen O *et al.* geoR: analysis of geostatistical data. 2023. http://www.leg.ufpr.br/geoR/ (27 March 2024, date last accessed)

Ruiz J, Abascal FJ, Bach P, et al. Bycatch of the European, and associated flag, purse-seine tuna fishery in the Indian Ocean for the period
2008-2017. IOTC-2018-WPEB14-15. Cape Town: IOTC Working Party on Ecosystems and Bycatch (WPEB), 2018.

Shono H. Application of the Tweedie distribution to zero-catch data in CPUE analysis. *Fish Res* 2008;93:154-62.

Sokolova M, Mompó Alepuz A, Thompson F *et al*. A deep learning approach to assist sustainability of demersal trawling operations. *Sustainability* 2021;13:12362.

Stock BC, Ward EJ, Eguchi T *et al*. Comparing predictions of fisheries bycatch using multiple spatiotemporal species distribution model frameworks. *Can J Fish Aquat Sci* 2020;77:146-63.

Valliant R, Dorfman AH, Royall RM. Finite population sampling and inference: a prediction approach. New York, NY: John Wiley & Sons, Inc., 2000.

Wain G, Guéry L, Kaplan DM *et al*. Quantifying the increase in fishing efficiency due to the use of drifting FADs equipped with echosounders in tropical tuna purse seine fisheries. *ICES J Mar Sci* 2021;78:235-45. https://doi.org/10.1093/icesjms/fsaa216

Wood SN. Generalized Additive Models: An Introduction with R. Boca Raton, FL: CRC Press/Taylor & Francis Group, 2017.

Yates LA, Aandahl Z, Richards SA *et al*. Cross validation for model selection: a review with examples from ecology. *Ecol Monogr* 2023;93:e1557. https://doi.org/10.1002/ecm.1557

*Handling Editor: Ruben Roa-Ureta*
2008-2017. IOTC-2018-WPEB14-15. Cape Town: IOTC Working Party on Ecosystems and Bycatch (WPEB), 2018.

Shono H. Application of the Tweedie distribution to zero-catch data in CPUE analysis. *Fish Res* 2008;93:154–62.

Sokolova M, Mompó Alepuz A, Thompson F *et al*. A deep learning approach to assist sustainability of demersal trawling operations. *Sustainability* 2021;13:12362.

Stock BC, Ward EJ, Eguchi T *et al*. Comparing predictions of fisheries bycatch using multiple spatiotemporal species distribution model frameworks. *Can J Fish Aquat Sci* 2020;77:146–63.

Valliant R, Dorfman AH, Royall RM. Finite population sampling and inference: a prediction approach. New York, NY: John Wiley & Sons, Inc., 2000.

Wain G, Guéry L, Kaplan DM *et al*. Quantifying the increase in fishing efficiency due to the use of drifting FADs equipped with echosounders in tropical tuna purse seine fisheries. *ICES J Mar Sci* 2021;78:235–45. https://doi.org/10.1093/icesjms/fsaa216

Wood SN. Generalized Additive Models: An Introduction with R. Boca Raton, FL: CRC Press/Taylor & Francis Group, 2017.

Yates LA, Aandahl Z, Richards SA *et al*. Cross validation for model selection: a review with examples from ecology. *Ecol Monogr* 2023;93:e1557. https://doi.org/10.1002/ecm.1557

*Handling Editor: Ruben Roa-Ureta*