Co-management of a high-value species with territorial use rights for fisheries: a spatial bioeconomic approach with environmental variability

INTRODUCTION

Conventionally, fisheries management has been given a monospecific and biological approach based on the effect of fishing on the population dynamics of a target species (Ulrich et al. 2002Ulrich C., Le Gallic B., Dunn M.R., Gascuel D. 2002. A multi-species multi-fleet bioeconomic simulation model for the English Channel artisanal fisheries. Fish. Res. 58: 379-401. https://doi.org/10.1016/S0165-7836(01)00393-9 , Lewy and Vinther 2004Lewy P., Vinther M. 2004. A stochastic age-length-structured multispecies model applied to North Sea stocks. Ices C.M. 33: 1-33., Kell et al. 2006Kell L.T., Pilling G.M., Kirkwood G.P. et al. 2006. An evaluation of multi-annual management strategies for ICES roundfish stocks. ICES J. Mar. Sci. 63: 12-24. https://doi.org/10.1016/j.icesjms.2005.09.003 ), without considering that fisheries management is regularly characterized by multiple objectives, which include a range of environmental, social and economic factors (Erisman et al. 2011Erisman B.E., Allen L.G., Claisse J.T., et al. 2011. The illusion of plenty: Hyperstability masks collapses in two recreational fisheries that target fish spawning aggregations. Can. J. Fish. Aquat. Sci. 68: 1705-1716. https://doi.org/10.1139/f2011-090 , FAO 2018FAO 2018. El estado mundial de la pesca y la acuicultura 2018. Cumplir los objetivos de desarrollo sostenible. Organización de las Naciones Unidas para la Alimentación y la Agricultura., Rome., Hilborn 2011Hilborn R. 2011. Future directions in ecosystem based fisheries management: A personal perspective. Fish. Res. 108: 235-239. https://doi.org/10.1016/j.fishres.2010.12.030 ).

In addition, some fisheries have been commercially exploited above the maximum sustainable yield level, thus leading to a depletion in stock renewal (FAO 2018FAO 2018. El estado mundial de la pesca y la acuicultura 2018. Cumplir los objetivos de desarrollo sostenible. Organización de las Naciones Unidas para la Alimentación y la Agricultura., Rome., Martinet et al. 2007Martinet V., Thébaud O., Doyen L. 2007. Defining viable recovery paths toward sustainable fisheries. Ecol. Econ. 64: 411-422. https://doi.org/10.1016/j.ecolecon.2007.02.036 ). This is the case of Haliotis corrugata W. Wood, 1828, an abalone from the western region of the Baja California Peninsula. H. corrugata is a gastropod mollusc that inhabits the area from the intertidal zone to rocky reefs up to 27 m deep. This species is one of the mainstays of the abalone fishery in Mexico, which dates back to the 19th century. This activity operates through territorial use rights for fisheries (TURFs), by which groups are granted exclusive privileges to fish in geographically designated fishing grounds. Since 1996, the National Fisheries Institute (INAPESCA) has managed this fishery based on catch quota recommendations determined by a risk analysis of two reference points derived from the dynamic biomass model (Muciño Díaz et al. 2000Muciño Díaz M., Sierra Rodríguez P., Vélez J.A., et al. 2000. Abulón. In: INP (ed), Sustentabilidad y Pesca Responsable En México: Evaluación y Manejo. pp. 217-262.); however, the stock has not been satisfactorily recovered. There are many hypotheses on the causes of this depletion in the stock, including overfishing, illegal and unregulated fishing or a combination of these factors (Castro-Ortiz and Guzmán del Próo 2018Castro-Ortiz J.L., Guzman del Proo S.A. 2018. Efecto del clima en las pesquerías de abulón y langosta espinosa en Baja California, Mexico. Oceánides 33: 13-25. https://doi.org/10.37543/oceanides.v33i2.219 , Gutiérrez-González 2012Gutiérrez-González J.L. 2012. Diagnóstico sobre la disminución de las poblaciones de abulón en la costa occidental de la península de Baja California y estrategias para atenuar los impactos negativos. Inf. Técnico SAGARPA-CONACyT 26., Ponce-Díaz 2008Ponce-Díaz G. 2008. Uso de los recursos marinos 1940-2003. In: SEMARNAT (ed), El Sa- Queo a La Conservación: Historia Ambiental Contemporánea de Baja California Sur, 1940-2003, México. Universidad Autonoma de Baja California Sur, pp. 279-336.).

Therefore, since 2017, the fishery has had a moratorium under an agreement between the resource users and the fishery managers. Recent population assessments indicate a slight recovery of the stock, perhaps favoured by zero fishing mortality and non-high variable environmental conditions; after the regime change in the mid-1970s, there have been no recent strong El Niño or La Niña events that affect the benthic community by decreasing the availability of food (Castro-Ortiz and Guzmán del Próo 2018Castro-Ortiz J.L., Guzman del Proo S.A. 2018. Efecto del clima en las pesquerías de abulón y langosta espinosa en Baja California, Mexico. Oceánides 33: 13-25. https://doi.org/10.37543/oceanides.v33i2.219 , Guzmán del Próo et al. 2003Guzmán del Próo S.A., Carreón-Palau L., Belmar-Pérez J., et al. 2003. Effects of the ‘EL Niño’ event on the recruitment of benthic invertebrates in Bahía Tortugas, Baja California Sur. Geofis. Int. 42: 429-438. https://doi.org/10.22201/igeof.00167169p.2003.42.3.929 ).

Models based only on time-dynamic assumptions are not suitable for the low-mobility abalone, because this species does not fulfil model assumptions of 1) homogeneous distribution, 2) perfectly mixed ages, 3) uniformly applied fishing effort, and 4) ability of abalone to redistribute according to 1 and 2 after the fishing effort has been applied. To avoid overestimating the productive potential of the stock, it is necessary to consider that not only the fishing effort but also the abundance of organisms (patchy distribution), their size and their age structure are heterogeneous. Therefore, management strategies should be based on a spatial age-structured bioeconomic model (Anderson and Seijo 2010Anderson L., Seijo J.C. 2010. Bioeconomics of Fisheries Management. Wiley-Blackwell., Sanchirico and Wilen 1999Sanchirico J.N., Wilen J.E. 1999. Bioeconomics of Spatial Exploitation in a Patchy Environment. J. Environ. Econ. Manage. 37: 129-150. https://doi.org/10.1006/jeem.1998.1060 , Seijo and Caddy 2008Seijo J.C., Caddy J.F. 2008. Port location for inshore fleets affects the sustainability of coastal source-sink resources: Implications for spatial management of metapopulations. Fish. Res. 91: 336-348. https://doi.org/10.1016/j.fishres.2007.12.020 ).

The yellow abalone fishery and its co-management were taken as a case study to solve the above assumptions. This fishery is characterized by a collective TURF for extraction, capture and commercial exploitation with co-management strategies based on a variable annual catch quota per species and fishing zone, each with economic consequences. The management strategies established in the law are as follows: effort control at maximum sustainable yield; minimum catch size per species and fishing zone; fixed temporary reproductive closure per zone; regulation of fishing gear and methods; and estimated reference points based on management objectives (DOF 1993DOF 1993. Norma Oficial Mexicana 005-PESC-1993, para regular el aprovechamiento de las poblaciones de las distintas especies de abulón en aguas de jurisdicción federal de la Península de Baja California., 2018DOF 2018. Carta Nacional Pesquera 2017. D. Of. la Fed. 8.).

Concerning bioeconomic and ecological-economic fisheries models, in a review of 35 models used worldwide Nielsen et al. (2018)Nielsen J., Thunberg E., Holland D.S., et al. 2018. Integrated ecological-economic fisheries models-Evaluation, review and challenges for implementation. Fish Fish. 19: 1-29. https://doi.org/10.1111/faf.12232 suggest that stakeholders should be involved in considering alternative management strategies and understanding the relevant elements of the fishery under study. It is also important to present results understandably to the fishing community and fisheries managers.

It is therefore imperative to analyse the fishery through management strategy evaluation (MSE) (Amar et al. 2008Amar Z.T., Punt A., Dorn M. 2008. The Management Strategy Evaluation Approach and the Fishery for Walleye Pollock in the Gulf of Alaska 317-346. https://doi.org/10.4027/rgsfcc.2008.18 , Hoshino et al. 2012Hoshino E., Milner-Gulland E.J., Hillary R.M. 2012. Bioeconomic adaptive management procedures for short-lived species: A case study of Pacific saury (Cololabis saira) and Japanese common squid (Todarodes pacificus). Fish. Res. 121-122: 17-30. https://doi.org/10.1016/j.fishres.2012.01.007 , Nielsen et al. 2018Nielsen J., Thunberg E., Holland D.S., et al. 2018. Integrated ecological-economic fisheries models-Evaluation, review and challenges for implementation. Fish Fish. 19: 1-29. https://doi.org/10.1111/faf.12232 , Punt et al. 2016Punt A.E., Butterworth D.S., de Moor C.L., et al. 2016. Management strategy evaluation: Best practices. Fish Fish. 17: 303-334. https://doi.org/10.1111/faf.12104 ), considering a more suitable model to determine the rate of exploitation required to achieve the target and limit bioeconomic reference points. An age-structured dynamic spatial bioeconomic model was developed to evaluate alternative management strategies to allow the stock to recover to a target level, incorporating risk and uncertainty determined by environmental variability associated with climate change. In addition to evaluating management strategies, it is essential to take up the approach and analysis conducted by Caddy and Seijo (1998)Caddy J.F., Seijo J.C. 1998. Application of a spatial model to explore rotating harvest strategies for sedentary species. Can. Spec. Publ. Fish. Aquat. Sci. 125: 359-365. regarding the rationale behind rotating harvest schemes for stocks where dynamic pool assumptions are inappropriate. The rotational harvest schemes are frequently used in fisheries management of sessile or sedentary stocks to give some specified level of stock protection and help alleviate the effect of growth and recruitment overfishing (Caddy 1993Caddy J.F. 1993. Background concepts for a rotating harvesting strategy with particular reference to the Mediterranean red coral, Corallium rubrum. Mar. Fish. Rev. 55: 10-18., DEEDI 2011DEEDI 2011. Evaluating the Effectiveness of the Rotational Zoning Scheme for the Queensland East Coast Beche-de-mer Fishery., Kewes et al. 2014Kewes T., Plagányi É., Murphy N. et al. 2014. Evaluating rotational harvest strategies for sea cucumber fisheries.). The present study aims to answer the following research questions: 1) Is any alternative management strategy more likely to meet the biological and economic objectives? (2) Given the prevailing environmental variability, what is the risk of falling below target and limit reference points?

MATERIALS AND METHODS

Spatial bioeconomic model

 ⌅

Management strategies were evaluated using a spatial bioeconomic model (SBEM) (Anderson and Seijo 2010Anderson L., Seijo J.C. 2010. Bioeconomics of Fisheries Management. Wiley-Blackwell., Seijo and Caddy 2008Seijo J.C., Caddy J.F. 2008. Port location for inshore fleets affects the sustainability of coastal source-sink resources: Implications for spatial management of metapopulations. Fish. Res. 91: 336-348. https://doi.org/10.1016/j.fishres.2007.12.020 ). This model simulates the dynamics of an age-structured population with a heterogeneous distribution for a single species: H. corrugata. The distribution area of the stock was divided into 625 cells in a 25×25 array, each covering an area of 0.25 km² for a total of 156 km². The spatial distribution of stock abundance was obtained through the assessments in the fishing banks from 2000 to 2017 carried out by the National Fisheries Institute (INAPESCA). This database contains the number of organisms per 50 m² transect (sample unit), geographically georeferenced using a global positioning system. The database has 21576 vectors, with the following information: Year, Abundance (Number of organisms), Zone, X-coordinate and Y-coordinate (INAPESCA 2019INAPESCA. 2019. Base de datos electrónica del proyecto Bentónicos del INAPESCA.). To represent and compare a continuous spatial density for the year in which the historical series begins (2000) and the year in which the moratorium starts (2017), the inverse distance weighted (IDW) interpolation method was applied through a geographic information system (QGIS.org 2022QGIS.org. 2022. QGIS Geographic Information System.).

The commercial catch was included in the model through a database that incorporates the number of organisms captured, thus generating a specific spatially explicit harvest matrix from the year 2000 to the year 2017. The H. corrugata harvest database has 35513 vectors, with the following information. Year, Zone, Subzone, X-coordinate, Y-coordinate and number of organisms captured (Progreso 2020Progreso S. 2020. Base de datos de captura histórica de la SCPP Progreso.).

The growth parameters incorporating environmental variability and the 17 ages (species longevity) to be considered in the spatial model correspond to H. corrugata on the north Pacific coast of Mexico. Parameters are taken from Vargas-López et al. (2021)Vargas-López V.G., Vergara-Solana F., Arreguín-Sánchez F. 2021. Effect of environmental variability on the individual growth of yellow abalone (Haliotis corrugata) and blue abalone (Haliotis fulgens) in the Mexican Pacific. Reg. Stud. Mar. Sci. 46: 101877. https://doi.org/10.1016/j.rsma.2021.101877 . The model functions and parameters are presented in Table 1. The heterogeneous distribution in spatial recruitment was modelled using the recruitment function of Beverton and Holt (1957)Beverton R., Holt S.J. 1957. On the Dynamics of Exploited Fish Populations. Great Britain, Fisheries Investigation Series. https://doi.org/10.2307/1440619 , multiplied by a negative binomial function (ɛ=15, µ=5), which allows spatially explicit patches to be generated with a probability of zero recruitment (Anderson and Seijo 2010Anderson L., Seijo J.C. 2010. Bioeconomics of Fisheries Management. Wiley-Blackwell.). Additionally, this function has been used in simulation works of sedentary species that colonize different sites (González-Durán et al. 2018González-Durán E., Hernández-Flores A., Seijo J.C., et al. 2018. Bioeconomics of the Allee effect in fisheries targeting sedentary resources. ICES J. Mar. Sci. 75: 1362-1373. https://doi.org/10.1093/icesjms/fsy018 , Seijo et al. 2004Seijo J.C., Pérez E.P.B., Caddy J.F.C. 2004. A simple approach for dealing with dynamics and uncertainty in fisheries with heterogeneous resource and effort distribution. Mar. Freshw. Res. 249-256. https://doi.org/10.1071/MF04040 , Seijo and Caddy 2008Seijo J.C., Caddy J.F. 2008. Port location for inshore fleets affects the sustainability of coastal source-sink resources: Implications for spatial management of metapopulations. Fish. Res. 91: 336-348. https://doi.org/10.1016/j.fishres.2007.12.020 ). Because of the highly selective nature of the fishery, no fishing mortality on sub-legal individuals occurs. An excel sheet developed by Anderson and Seijo (2010)Anderson L., Seijo J.C. 2010. Bioeconomics of Fisheries Management. Wiley-Blackwell. was adapted to the specific spatial characteristics of the abalone fishery in the study region to conduct the spatial management simulations with the mathematical models described in Table 2.

Table 1.  - Parameters of the SBEM of H. corrugata.

Parameters	Symbol	Value	Unit of measurement	Source
Maximum age of species	λ	17	years	1
Age at first maturity		5	years	1
Age at first capture		5	years	1
Parameter t0 of the growth	t 0	-0.55	proportion	1
Natural mortality coefficient	M	0.37	year-1	2
Parameter k of von Bertalanffy growth	k	0.35	year-1	1
Maximum length	L ∞	15.1	cm	1
Maximum weight	W ∞	5465	g	1
Alpha parameter of B-H recruitment function	α	329351	recruits	2
Beta parameter of B-H recruitment function	β	300	tonnes	2
L50% gear retention	L 50%	13.0	cm	2
L75% gear retention	L 75%	14.5	cm	2
s1 parameter of selectivity	s1	4.14	-	2
s2 parameter of selectivity	s2	0.32	-	2
Area swept per day	a	0.228	km2	2
Total area of stock distribution	area	32	km2	2
Price of specie	p	41180	$/tonnes	2
Probability of capture	c	0.9	(0.1)	2
Exit/entry parameter	φ	0.0001	vessel/$MX	2
Alpha parameter of age-specific natural mortality		0.24	Year-1	2
Beta parameter of age-specific natural mortality		0.68	-	2
Initial number of vessels	V 0	25	vessels	2
Average fishing trips per vessel	FD	30	days/year	2
Discount rate	td	0.05	Year-1	2
Length of trip	L	1	Days	2
Steaming speed of the vessel	v	30	km/day	2
Operating cost of a vessel steaming	C 1	120	$/day	2
Operating cost of vessel fishing	C 2	70	$/day	2
Fixed costs	FC	100	$/year/vessel	2
Parameter ᵋ of the negative binomial distribution	ᵋ	15	-	2
Parameter µ of the negative binomial distribution	µ	5	-	2

¹Vargas-López et al. (2021)Vargas-López V.G., Vergara-Solana F., Arreguín-Sánchez F. 2021. Effect of environmental variability on the individual growth of yellow abalone (Haliotis corrugata) and blue abalone (Haliotis fulgens) in the Mexican Pacific. Reg. Stud. Mar. Sci. 46: 101877. https://doi.org/10.1016/j.rsma.2021.101877 ² This study

Table 2.  - Spatial bioeconomic equations for the H. corrugata fishery in the study area.

Description	Equation	Definition	Reference
Recruitment	$R_{s,t}=\frac{{\Sigma }_s{SSB}_{s,t^{\alpha }}}{\beta +{\Sigma }_s{SSB}_{s,t}}P\left(s,d\right)$	${\Sigma }_s{SSB}_{s,t}$ = total spawning biomass in time ${SSB}_{s,t}$ = ${\Sigma }_{i=sm}^{\lambda }{X}_i,\alpha$ = maximum annual recruitment $sm$ = age of sexual maturity $\beta$ = total spawning biomass for $\alpha /2$	(Seijo et al. 2004Seijo J.C., Pérez E.P.B., Caddy J.F.C. 2004. A simple approach for dealing with dynamics and uncertainty in fisheries with heterogeneous resource and effort distribution. Mar. Freshw. Res. 249-256. https://doi.org/10.1071/MF04040 )
Age-specific natural mortality	$M_i\frac{\mathrm{\varphi }{}_1+\mathrm{\varphi }{}_2}{i}$	$\mathrm{\varphi }{}_1$ = alpha parameter of age-specific natural mortality $\mathrm{\varphi }{}_2$ = beta parameter of age-specific natural mortality	(Caddy 2018Caddy J.F. 2018. Conserving spawners and harvesting juveniles: Is this a better alternative to postponing capture until sexual maturity? In: Seijo J.C., Sutinen J.G. (eds), Advances in Fisheries Bioeconomics. Routledge, Taylor & Francis, London, UK, p. 195. https://doi.org/10.4324/9780203705780 , 1991Caddy J.F. 1991. Death rates and time intervals: is there an alternative to the constant natural mortality axiom? Rev. Fish Biol. Fish. 1: 109-138. https://doi.org/10.1007/BF00157581 )
Survival of cohort	$\frac{d{N}_{i,s}}{dt}=-\left(F_{i,s,t}+M\right)N_{i,s,t}$	$N_{i,s,t}$ = number of individuals of age i in site s in time t $F_{i,s,t}$ = specific mortality at age i in site s in time t $M$ = instantaneous natural mortality rate	(Anderson and Seijo 2010Anderson L., Seijo J.C. 2010. Bioeconomics of Fisheries Management. Wiley-Blackwell.)
Fishing mortality	$F_{i,s,t}=E_{s,t}{q}_i$	$E_{s,t}$ = total fishing effort in site s in time t $q_i$ = catchability coefficient specific to the cohort	(Rikhter and Efanov 1976Rikhter V.A., Efanov V.N. 1976. On one of the approaches to estimation of natural mortality of fish populations. Int. Comm. Northwest Atl. Fish. VI: 1-12.)
Catchability coefficient	$q_i=-ln\left[1-\left(\frac{a{SEL}_{i}c}{Area}\right)\right]$	$a$ = area swept per day in km2 $Area$ = area of stock distribution in km2 $c$ = probability of capture	(Baranov 1918Baranov F.I. 1918. On the question of the biological basis of fisheries, 1st ed. Izvestiya Nauchno-Issled Institut., Sparre and Venema 1998Sparre P., Venema S.C. 1998. Introduction to tropical fish stock assessment. Pt. 1: Manual. Pt. 2: Exercises. Introd. to Trop. fish Stock assessment. Pt. 1 Manual. Pt. 2 Exerc.)
Selectivity	${Sel}_i= \frac{1}{1+e^{s_1-s_2*L_i}}$	$s_{1}from and s_2$   Sparre and Venema (1998)Sparre P., Venema S.C. 1998. Introduction to tropical fish stock assessment. Pt. 1: Manual. Pt. 2: Exercises. Introd. to Trop. fish Stock assessment. Pt. 1 Manual. Pt. 2 Exerc.	(Sparre and Willman 1993Sparre P.J., Willman R. 1993. Software for bio-economic analysis of fisheries. BEAM 4. Analytical bio-economic simulation of space-structured multispecies and multi-fleet fisheries. (No. Vol. 186).)
S1 ; S2	$L_{50\%}ln\left(\frac{3}{L_{75\%}-L_{50\%}}\right)$ ∀ $s_2=\frac{s_1}{L_{50\%}}$	$L_{50\%}$ = length at 50% gear retention $L_{75\%}$ = length at 75% gear retention	(Sparre and Venema 1998Sparre P., Venema S.C. 1998. Introduction to tropical fish stock assessment. Pt. 1: Manual. Pt. 2: Exercises. Introd. to Trop. fish Stock assessment. Pt. 1 Manual. Pt. 2 Exerc.)
Total biomass available	$B_{s,t}=\sum _{i=1}^{i=k}{N}_{i,s,t}{W}_i$	$W_i$ = weight of individuals at age	(Anderson and Seijo 2010Anderson L., Seijo J.C. 2010. Bioeconomics of Fisheries Management. Wiley-Blackwell.)
Total profits per vessel per year	${\pi }_t= \sum _s\left({py}_{st}-C_{st}{E}_{st}\right)-FC*V_t$	${py}_{st}$ = total revenues per vessel in site s in time t $E_{st}$ = fishing effort in fishing days $FC$ = fixed costs per vessel $V_t$ = number of vessels in time t	(Anderson and Seijo 2010Anderson L., Seijo J.C. 2010. Bioeconomics of Fisheries Management. Wiley-Blackwell.)
Spatial allocation of fishing effort	$E_{s,t+1}=\frac{quasi {\pi }_{s,t}}{{\sum }_{s}quasi {\pi }_{s,t}}{V}_{t+1}fd$	fd = average number of fishing days per vessel per year $quasi {\pi }_{s,t}$ = quasi-profits of the variable costs of a vessel fishing in site s in time t	(Anderson and Seijo 2010Anderson L., Seijo J.C. 2010. Bioeconomics of Fisheries Management. Wiley-Blackwell., Seijo and Caddy 2008Seijo J.C., Caddy J.F. 2008. Port location for inshore fleets affects the sustainability of coastal source-sink resources: Implications for spatial management of metapopulations. Fish. Res. 91: 336-348. https://doi.org/10.1016/j.fishres.2007.12.020 )
Quasi-rents	$quasi {\pi }_{s,t}={py}_{st}- C_{st}{E}_{st}$		-
Variable costs	$C_{st}= \frac{\frac{D_s}{v}{c}_1+(L-\frac{D_s}{v})c_2}{L}$	$D_s$ = round trip distance between port of origin and fishing site s (km) $v$ = steaming speed of vessels (km/day) $c_1$ = cost per day of operating a vessel when steaming ($/day) $c_2$ = cost per day of operating a vessel when fishing ($/day) $L$ = average length of trip in days	(Anderson 2002Anderson L. 2002. A comparison of the utilization of stocks with patchy distribution and migration under open access and marine reserves: an extended analysis. Mar. Resour. Econ. 17: 269-289. https://doi.org/10.1086/mre.17.4.42629370 )
Spatial yield	$y_{st}=\sum _i{X}_{ist}\left[\frac{F_{ist}}{F_{ist}+M}\right](1-e^{\left[-\left(F_{ist}+M\right)\right]})$		(Seijo and Caddy, 2008Seijo J.C., Caddy J.F. 2008. Port location for inshore fleets affects the sustainability of coastal source-sink resources: Implications for spatial management of metapopulations. Fish. Res. 91: 336-348. https://doi.org/10.1016/j.fishres.2007.12.020 )
Minimum catch per unit of effort	${CPUEmin}_s=\frac{\left[\frac{\frac{D_s}{v}{c}_1+\left(L-\frac{D_s}{v}\right)c_2}{L}\right]}{p}$		(Anderson and Seijo 2010Anderson L., Seijo J.C. 2010. Bioeconomics of Fisheries Management. Wiley-Blackwell.)
Dynamic yield per unit of effort	${CPUE}_{st}= \sum _i\left(q_i{X}_{ist}\right)$		(Anderson and Seijo 2010Anderson L., Seijo J.C. 2010. Bioeconomics of Fisheries Management. Wiley-Blackwell.)
Number of vessels per year	$V_{t+1}= V_t+ \varnothing \left[\sum \left(p{Y}_{st}-C_{st}\right)-FC{V}_t\right]$	$\varnothing$ = enter/exit parameter	(Smith 1969Smith V.L. 1969. On Models of Commercial Fishing. J. Polit. Econ. 77: 181-198. https://doi.org/10.1086/259507 )
Net present value	$VPN=\underset{y=0}{\overset{Y}{\int }}\prod _y{e}^{{-\delta }_y}$	Y = simulation horizon ${\delta }_y$ = discount rate

This abalone fishery is managed by catch quota recommendations and in 2010 caught about 24 tonnes with an effort in fishing trips of 1125. As observed in other studies (e.g. Sanchirico and Wilen 1999Sanchirico J.N., Wilen J.E. 1999. Bioeconomics of Spatial Exploitation in a Patchy Environment. J. Environ. Econ. Manage. 37: 129-150. https://doi.org/10.1006/jeem.1998.1060 ; Cabrera and Defeo 2001Cabrera J.L., Defeo O. 2001. Daily bioeconomic analysis in a multispecific artisanal fishery in Yucatan, Mexico. Aquat. Living Resour. 14: 19-28. https://doi.org/10.1016/S0990-7440(00)01094-9 ; Hernández-Flores et al. 2018Hernández-Flores A., Cuevas-Jiménez A., Poot-Salazar A., et al. 2018. Bioeconomic modeling for a small-scale sea cucumber fishery in Yucatan, Mexico. PLoS ONE 13: 1-17. https://doi.org/10.1371/journal.pone.0190857 ), the spatial allocation of fishing intensity (effort per unit of area) was based on the quasi-rents of the variable costs obtained in alternative fishing sites over time. The spatial allocation of effort over time was allocated over space in proportion to the site-specific profits obtained in the previous periods; when the income fell to zero in any area, the function stopped allocating fishing effort to it (Caddy and Seijo 1998Caddy J.F., Seijo J.C. 1998. Application of a spatial model to explore rotating harvest strategies for sedentary species. Can. Spec. Publ. Fish. Aquat. Sci. 125: 359-365.). Thus, the number of daily fishing trips in each management strategy is determined by changes in abundance in the resource’s distribution area, the costs of fishing in alternative sites and the price of abalone. The Vt dynamic is calculated by numerically integrating (using Euler numerical integration with DT=1 in this case) the spatially adapted Vernon Smith (1969)Smith V.L. 1969. On Models of Commercial Fishing. J. Polit. Econ. 77: 181-198. https://doi.org/10.1086/259507 function. A vessel makes one fishing trip per day, targeting only one species. Therefore, a single commercially exploited species determines the total costs and profits. The yellow abalone fishery is assumed to be price-taking, so its harvest does not affect the corresponding market prices. To simplify the analysis, constant prices were assumed over the simulation run. This dynamic bioeconomic model allows vessel exit in case of negative profits and restricts fishing not exceeding the maximum catch observed in 2010. Employment effects are negligible because community fishers have access rights to another high-value species (red spiny lobster, Panulirus interruptus), so they would not become unemployed when effort is at a level that maximizes the present value of resource rent, which involves less employment than operating at maximum sustainable yield.

To calibrate the SBEM, a comparison of the observed yield (Y_obs) and the calculated yield (Y_cal) for the first period (2000-2017) was carried out (Fig. 1). Statistical comparison of and was performed using the two-sample Kolmogorov-Smirnov (KS) test. The KS test statistic is D=0.333 and the corresponding p-value = 0.27. Since the p-value is greater than 0.05, we accept the null hypothesis. This indicates that the Y_obs and Y_cal datasets do not exhibit statistically significant differences. This allows us to infer that the suitable sensitivity of the SBEM foresaw a decrease in biomass and therefore calculated yields appropriate to this trend.

Fig. 1.  - Observed yield and yield calculated by the SBEM (A); trajectories of biomass (B), yield (C) and resource rent per vessel (D) forecasted by the SBEM using MSE. (grey and coloured area are uncertainty associated with simulations).

Once the SBEM was calibrated, management strategies for the yellow abalone fishery in the Mexican North Pacific were simulated and compared. The comparison between management strategies was based on the effect on biomass, predicted yield and present value of resource rent. The strategies evaluated are described in Table 3.

Table 3.  Management strategies considered in this study.

Management Strategy	Name	Description
Emsy	Effort at maximum sustainable yield	Status quo. This is based on the Mexican government’s current and official fishing regulations, which explicitly state that the abalone fishery effort must operate at maximum sustainable yield (DOF, 2018DOF 2018. Carta Nacional Pesquera 2017. D. Of. la Fed. 8.).
EmaxNPV	Effort at maximum present value of resource rent	Fisheries managers can adjust the overall level of fishing effort such that present value of resource rent is maximized and biomass is higher than the one resulting from operating at MSY.
Emin	Community-determined minimum fishing effort when the fishery reopens	Minimum level of effort to obtain quasi-profits of the variable costs of fishing equal to or above the ones currently obtained from the spiny lobster fishery.

At the request by resource users in this co-managed fishery to lift the moratorium on the fishery, the aim was to identify the minimum effort (fishing days) at which the fishers can obtain an above-zero resource rent to cover the operating cost of four vessels and their opportunity cost of labour of moving to another high-value species such as the red spiny lobster Panulirus interruptus. As an assumption in the simulation period, the fishery management authority is considering this minimum effort when it reopens the fishery.

Simulations using these management strategies began with the assumption of lifting the moratorium on the fishery starting in 2023 and continuing for a simulation period of 17 years until 2040. This period is equivalent to one life cycle of H. corrugata.

RESULTS

Spatial distribution and density

 ⌅

To represent the variation in abalone density, two plots were made using IDW interpolation (Fig. 2A and B). At the beginning of the historical series (2000), there was extensive coverage of abalone in the fishing zone; in 2017, this coverage fell considerably, as shown in Figure 1A and B, and the average density per sample unit decreased from 0.144 to 0.062 ind/50m² during that period. These changes and the reduction in density were the reason for the moratorium agreement for the fishery.

Fig. 2.  Spatial distribution of yellow abalone in the study area as observed in 2000 (A) and 2017 (B).

Management strategy evaluation

 ⌅

When performing one thousand simulations of the calculated values for the observed period, incorporating uncertainty in the parameter k’ of the von Bertalanffy growth function, variability in the calculated values was observed; this was mainly determined by the wide range of the assumed value (k’) in the uncertainty analysis (Fig. 1A). It can be inferred that during the period 2004 to 2010, the values of Y_obs and Y_cal were very similar. After this period, there was a difference to consider. As of 2011, the SBEM was already calculating lower catch values than those observed. It is noteworthy that for 2013, the Y_obs coincided with the outlier value of the Y_cal trajectory calculated for that year. From 2011 to 2016, the Y_obs was above the values calculated through simulations. The SBEM thus suggests that catches from 2013 to 2017 decreased from approximately 15 to 8 t, a situation leading to closure of the fishery after 2017.

The biomass levels projected by the SBEM considering the MSE are presented in Figure 1B. This graph clearly shows the differences between biomass trajectories. Different levels of fishing effort determined by the management strategies evaluated generate levels of final biomass that are important for consideration by the stakeholders.

In the simulation period, when the moratorium was lifted and harvesting of the resource began, a decrease in biomass levels was observed in the three management strategy trajectories. Subsequently, the dynamic catch quota effect was observed four years after reopening the fishery. Derived from this, the E_min management strategy tended to equilibrium biomass in less time than the other management strategies. The E_min and E_maxNPV management strategies allowed higher biomass levels than the E_msy management strategy at the end of the simulation period. As expected, E_min (lowest effort) was the management strategy in which the highest biomass level was observed at the end of the simulation.

The yield trajectories projected by the SBEM considering the three management strategies show decreasing trends, although in different magnitudes, towards the end of the simulation period. (Fig. 1C)

As expected, different levels of effort generated different levels of forecasted yield (Fig. 1C). E_msy predicted yields above E_maxNPV because E_msy operates in open access concerning the number of daily fishing trips per season (status quo). E_maxNPV has a catch quota restriction based on the assumption of not exceeding the maximum recommended quota in the observed period of the fishery. Nevertheless, it must maximize the economic rent generated by the resource. For this reason, the trajectory of this management strategy was lower throughout the simulation than E_msy but higher than E_min. The magnitude of the difference in yield trajectories should be recognized by authorities and fishers when they consider reopening the fishery due to the requirements in the number of vessels needed to catch the forecasted values: E_min predicted an initial yield of 9 t, and a final yield of 6 t, while, E_msy predicted an initial yield of 31 t and a final yield of 12 t. This management strategy suggests higher catch quotas than those recorded in the observed period.

To compare the resource rent for the alternative MSE, resource rent per vessel is likely to be considered as a decision variable by resource users and authorities. At the beginning of the simulation, mainly because of the low mobility, high catchability and consequently high value and low costs of the resource in the fishing operation, the resource rent generated by the fishery was 50% higher in E_maxNPV than in E_min and 75% higher than in E_msy (Fig. 1D). However, it gradually declined as the dynamic catch quotas developed. At the end of the simulation, resource rent per vessel in E_maxNPV and E_min were higher than resource rent per vessel in E_msy.

Other alternative discount rates could be used for different contexts to calculate the present value of resource rent. Table 7 shows the effect on present value of resource rent for the three options for three alternative rates of discount.

Table 7.  Effect on present value of resource rent for the three management strategies considering three alternative rates of discount.

Discount rate	Emsy	EmaxNPV	Emin
0.025	$526	$1347	$1101
0.050	$437	$1074	$867
0.075	$399	$956	$770

In Figure 3, a comparison of net present value (NPV) per vessel for the MSE is shown. The NPV was considerably higher in E_maxNPV, three times higher than that in E_msy. The high yield at the beginning of the simulation, the high value of the species, and the low total costs are the variables that determine this considerable difference. Another critical factor conditioning this high NPV is the spatial allocation of effort determined by the SBEM.

Fig. 3.  - Comparison of the net present value through the MSE.

It is crucial to compare NPV values per vessel, thus generating a fundamental decision criterion for fishers and authorities. Dividing E_msy NPV by 25 vessels, we obtained USD 436570 per vessel. In the case of E_min NPV divided by four vessels gave USD 866662 per vessel. In the long term, the E_min management strategy generated a higher NPV per vessel than E_msy, requiring a lower number of vessels and optimal results in final biomass and yield. In the case of E_maxNPV, the NPV value divided by the six vessels (six is the total number of vessels needed to perform 471 fishing trips in the fishery season) gave a total of USD 1073520 per vessel, which is the maximization of the NPV in the MSE.

Table 8 shows the management strategies, effort units, final biomass, final yield and final NPV per vessel per strategy at the end of the simulation period. This table offers clear visualization of the SBEM outputs, which implicitly include the fishery’s social, economic and biological considerations-crucial characteristics for decision-making.

Table 8.  Spatial bioeconomic model outputs from the MSE.

Strategy	Fishing days	Explotation rate (F)	Vessels*	B2040	Y2040	NPV** (000 USD)
Emin	196	0.01	4	354	5	867
EmaxNPV	471	0.02	6	312	9	1288
Emsy	1246	0.06	25	244	12	437

*The minimum number of vessels required to conduct the fishing days per strategy per season.**17-year calculation period with a 0.05 discount rate.

Monte Carlo Analyses and probabilities of exceeding the LRP and TRP

 ⌅

After generating 1000 simulations, we calculated the probability of B₂₀₄₀ falling below the LRP of B_min and the TRP of B_msy. In the case of resource rent, we calculated the probability of having an RR_pv greater than the LRP of RR_min and the TRP of RR_opt at the end of the simulation period (RR₂₀₄₀). The biomass at the level in which the fishery went to closure in 2017 (B_min: 190 t) and the minimum resource rent to cover the operating cost of one vessel and its opportunity cost of labour of moving to another high-value species (RR_min: USD 15000) were used as LRPs; the biomass at maximum sustainable yield (B_msy: 244 t) and a fisher-proposed optimum resource rent per vessel (50% higher than RR_min) (RR_opt: USD 23000) were used as TRPs (Figs 4 and 5).

Fig. 4.  - Risk (dark area) of falling below the biomass LRP and TRP at the end of the simulation period.

Fig. 5.  - Risk (grey area) of exceeding the LRP and TRP of RRpv at the end of the simulation period.

In the case of biomass, the three management strategies showed probabilities of falling below the TRP (dark area under the probability chart), but E_msy was the one that had the greatest risk of falling below it. Operating at this level of effort increased the risk (86%) that the biomass at the end of the simulation would fall below the desirable level point. In addition, with this strategy, there was also a 30% risk of falling below the LRP, the same biomass level that caused the closure of the fishery in 2017. The other two strategies involved zero risk of falling below this undesirable biomass level.

The resource rent is a crucial variable in fishermen’s and authorities’ decision-making. For this reason, two reference points were evaluated (TRP and LRP). Both E_min and E_maxNPV had a 100% probability (grey area under the probability chart) of being above the LRP. E_maxNPV was the strategy with the highest probability (47%) of exceeding the TRP of USD 23000 per vessel. E_msy was the strategy with a 0% probability of being above both reference points. In economic and sustainable terms, it is not a suitable strategy to be employed, because it shows a high risk of falling below biomass at maximum sustainable yield and it generates zero probabilities concerning the economic benefit that fishers could obtain from the resource in terms of reference points. A summary of the probabilities of exceeding LRP and TRP are shown in Table 8.

Once these reference points have been evaluated, as Anderson and Seijo (2010)Anderson L., Seijo J.C. 2010. Bioeconomics of Fisheries Management. Wiley-Blackwell. comment, the fishers and authorities (decision-makers) and their inherent attitude towards risk will determine which strategy should be implemented in the reopening of the fishery and whether to reduce risks of returning to an undesirable biomass level that would suggest another fishery closure. It is necessary to identify the strategy or strategies that provide resource users with the maximization of the economic rent generated by this species while at the same time avoiding overexploitation.

Table 9.  Probabilities of falling below the LRP and TRP for biomass (B₂₀₄₀) and exceeding the LRP and TRP for resource rent per vessel (RR_pv2040).

Strategy	Biomass (t)		RRpv (USD/year per vessel)
	LRP	TRP	LRP	TRP
	B<Bmin	B<Bmsy	RRpv>RRmin	RRpv>RRopt
	190	244	15000	23000
Emin	0	0.6	100	30
EmaxNPV	0	29	100	47
Emsy	30	86	0	0
Probabilities are expressed in percent.

DISCUSSION

Our results provide the methodological basis for evaluating the potential economic and stock recovery benefits of applying an SBEM. Furthermore, we analyse management strategies for an abalone fishery considering the risks and uncertainty of environmental variability associated with climate change. Like Nielsen et al. (2018)Nielsen J., Thunberg E., Holland D.S., et al. 2018. Integrated ecological-economic fisheries models-Evaluation, review and challenges for implementation. Fish Fish. 19: 1-29. https://doi.org/10.1111/faf.12232 , Seung and Waters (2006)Seung C., Waters E.C. 2006. A Review of Regional Economic Models for Fisheries Management in the U.S.A. Mar. Resour. Econ. https://doi.org/10.1086/mre.21.1.42629497 and Seijo et al. (1998)Seijo J.C., Defeo O., Salas S. 1998. Fisheries bioeconomics: theory, modelling and management. FAO. Fish. Tech. Pap. 108., we approached the management strategies and spatial data with the collaboration and suggestions of community fishers and fishery managers.

The application of spatial modelling in fisheries resources has been increasing since the initial work of Caddy (1975)Caddy J.F. 1975. Spatial Model for an Exploited Shellfish Population, and its Application to the Georges Bank Scallop Fishery. J. Fish. Res. Board Canada 32: 1305-1328. https://doi.org/10.1139/f75-152 and the research of fisheries economists (Holland and Brazee 1996Holland D.S., Brazee R. 1996. Marine Reserves for Fisheries Management. Mar. Resour. Econ. 11: 157-171. https://doi.org/10.1086/mre.11.3.42629158 , Holland et al. 2004Holland D.S., Sanchirico J.N., Curtis R.E., Hicks R.L. 2004. An introduction to spatial modeling in fisheries economics. Mar. Resour. Econ. 19: 1-6. https://doi.org/10.1086/mre.19.1.42629415 , Akpalu and Vondolia 2012Akpalu W., Vondolia G.K. 2012. Bioeconomic model of spatial fishery management in developing countries. Environ. Dev. Econ. 17: 145-161. https://doi.org/10.1017/S1355770X11000416 ), but few authors have used spatially explicit age-structured dynamic bioeconomic models (Seijo and Caddy 2008Seijo J.C., Caddy J.F. 2008. Port location for inshore fleets affects the sustainability of coastal source-sink resources: Implications for spatial management of metapopulations. Fish. Res. 91: 336-348. https://doi.org/10.1016/j.fishres.2007.12.020 , González-Durán et al. 2018González-Durán E., Hernández-Flores A., Seijo J.C., et al. 2018. Bioeconomics of the Allee effect in fisheries targeting sedentary resources. ICES J. Mar. Sci. 75: 1362-1373. https://doi.org/10.1093/icesjms/fsy018 , Hernández-Flores et al. 2018Hernández-Flores A., Cuevas-Jiménez A., Poot-Salazar A., et al. 2018. Bioeconomic modeling for a small-scale sea cucumber fishery in Yucatan, Mexico. PLoS ONE 13: 1-17. https://doi.org/10.1371/journal.pone.0190857 ). The impacts of climate change or other long-term changes in productivity can be approximated and examined within the MSE model. It is possible to include long-term trends in natural mortality, growth and recruitment that may be used to understand the likely effects of changes in productivity caused by climate change or other environmental drivers (Hordyk et al. 2017Hordyk A., Newman D., Carruthers T., Suatoni, L. 2017. Applying management strategy evaluation to California fisheries: case studies and recommendations 1-245. https://doi.org/10.1139/cjfas-2017-0482 ).

Bioeconomic models for managing fisheries globally have been used for a couple of decades (Pascoe et al. 2016Pascoe S., Kahui V., Hutton T., Dichmont C. 2016. Experiences with the use of bioeconomic models in the management of Australian and New Zealand fisheries. Fish. Res. 183: 539-548. https://doi.org/10.1016/j.fishres.2016.01.008 ). The use of MSE for abalone fisheries is also well documented (Harford et al. 2019Harford W.J., Dowling N.A., Prince J.D. et al. 2019. An indicator-based decision framework for the northern California red abalone fishery. Ecosphere 10. https://doi.org/10.1002/ecs2.2533 ). The abalone fishery in Mexico has been the subject of research regarding its population dynamics, stock assessment, reference points and the management of abalone stocks in the region. However, this is the first study that considers three important areas: economic, social and environmental sustainability in the North Pacific region, where many crucial fisheries are located.

This study confirms that abalone, like other semi-sessile resources, are highly vulnerable to overfishing (Ramírez-Rodríguez and Ojeda-Ruíz 2012Ramírez-Rodríguez M., Ojeda-Ruíz M.Á. 2012. Spatial management of small-scale fisheries on the west coast of Baja California Sur, Mexico. Mar. Policy 36: 108-112. https://doi.org/10.1016/j.marpol.2011.04.003 , Aburto and Stotz 2013Aburto J., Stotz W. 2013. Learning about TURFs and natural variability: Failure of surf clam management in Chile. Ocean Coast. Manag. 71: 88-98. https://doi.org/10.1016/j.ocecoaman.2012.10.013 , Hernández-Flores et al. 2018Hernández-Flores A., Cuevas-Jiménez A., Poot-Salazar A., et al. 2018. Bioeconomic modeling for a small-scale sea cucumber fishery in Yucatan, Mexico. PLoS ONE 13: 1-17. https://doi.org/10.1371/journal.pone.0190857 ), which is mainly due to its high value and low costs in the fishing operation. As mentioned by Herrera (2006)Herrera G.E. 2006. Benefits of spatial regulation in a multispecies system. Mar. Resour. Econ. 21: 63-79. https://doi.org/10.1086/mre.21.1.42629495 , spatial regulation is particularly beneficial when stocks are slow-growing and high-priced.

The MSE allows alternative strategies to be evaluated in addition to the control rules known by fishers and the corresponding authorities within a co-management scheme. E_msy is a strategy that recommends a higher effort at the beginning of the simulation than that observed in the historical series, and is likely to generate undesirable biomass levels. Alternatively, E_min and E_maxNPV offer an effort reduction of 85% and 63% of the maximum observed effort, respectively. By reducing the number of fishing trips, it is possible to increase long-term economic net benefits for the Mexican abalone fishery and to minimize the impact of fishing mortality in varying environmental conditions that have been shown to have a significant effect on growth and other biological processes of this resource (Ponce-Díaz 2008Ponce-Díaz G. 2008. Uso de los recursos marinos 1940-2003. In: SEMARNAT (ed), El Sa- Queo a La Conservación: Historia Ambiental Contemporánea de Baja California Sur, 1940-2003, México. Universidad Autonoma de Baja California Sur, pp. 279-336., Castro-Ortiz and Guzmán del Próo 2018Castro-Ortiz J.L., Guzman del Proo S.A. 2018. Efecto del clima en las pesquerías de abulón y langosta espinosa en Baja California, Mexico. Oceánides 33: 13-25. https://doi.org/10.37543/oceanides.v33i2.219 , Vargas-López et al. 2021Vargas-López V.G., Vergara-Solana F., Arreguín-Sánchez F. 2021. Effect of environmental variability on the individual growth of yellow abalone (Haliotis corrugata) and blue abalone (Haliotis fulgens) in the Mexican Pacific. Reg. Stud. Mar. Sci. 46: 101877. https://doi.org/10.1016/j.rsma.2021.101877 ). The above results from the MSE analysis indicate that adapting to possible effects of uncertainty due to climate change can be accomplished using, as a precautionary measure, a reduction of fishing effort in a strategy that maximizes the NPV of the fishery.

It is complicated to compare our results with those of other studies because there are no published references of the consequence of alternative management measures on spatially explicit fisheries like our study case on abalone. Nevertheless, the MSE demonstrates that effort limits could meet the management objectives for this stock. This may incentivize the development of mechanisms to manage the fishery using both input and output controls. Limiting the effort to E_min and E_maxNPV reduced overfishing of the resource, allowing some recovery of a heavily exploited fishery and producing higher catches and profits in the long term. This study indicates that under current regulations (status quo), dissipation of rent is generated for the fleet, and we conclude that E_msy could be indicative of overcapacity in this fishery (Anderson et al. 2015Anderson J.L., Anderson C.M., Chu J. et al. 2015. The fishery performance indicators: A management tool for triple bottom line outcomes. PLoS ONE 10: 1-20. https://doi.org/10.1371/journal.pone.0122809, Asche et al. 2009Asche F., Bjørndal T., Gordon D. V. 2009. Resource rent in individual quota fisheries. Land Econ. 85: 279-291. https://doi.org/10.3368/le.85.2.279 , Emery et al. 2017Emery T.J., Gardner C., Hartmann K., Cartwright I. 2017. Incorporating economics into fisheries management frameworks in Australia. Mar. Policy 77: 136-143. https://doi.org/10.1016/j.marpol.2016.12.018 ).

This study suggests that strategies E_min and E_maxNPV may help maintain the abalone fishery and yields in the long term. Several studies have reported that biomass associated with maximization of NPV is higher than that associated with MSY (McGarvey et al. 2016McGarvey R., Matthews J.M., Feenstra J.E. et al. 2016. Using bioeconomic modeling to improve a harvest strategy for a quota-based lobster fishery. Fish. Res. 183: 549-558. https://doi.org/10.1016/j.fishres.2016.05.005 , Punt et al. 2010Punt A.E., Deng R.A., Dichmont C.M. et al. 2010. Integrating size-structured assessment and bioeconomic management advice in Australia’s northern prawn fishery. ICES J. Mar. Sci. 67: 1785-1801. https://doi.org/10.1093/icesjms/fsq037 ). Others suggest that reference points lower than f_msy may be more suitable in terms of higher profits and safer biomass levels (Grafton et al. 2010Grafton R., Kompas T., Chu L., Che N. 2010. Maximum economic yield 273-280. https://doi.org/10.1111/j.1467-8489.2010.00492.x ; Da-Rocha et al. 2015Da-Rocha J.M., Gutiérrez M., Cerviño S. 2015. Reference Points on dynamic optimization: a versatile algorithm for mixed-fishery management with bioeconomic age-structured models. ICES J. Mar. Sci. 69: 660-669. https://doi.org/10.1093/icesjms/fss012 ; De Anda-Montañez et al. 2017De Anda-Montañez J.A., Salas S., Galindo-Cortes G. 2017. Tratando con dinámica e incertidumbre de pesquerías de pelágicos menores: Análisis bioeconómico de respuesta del administrador ante diferentes estrategias de manejo. Rev. Biol. Mar. Oceanogr. 52: 51-65. https://doi.org/10.4067/S0718-19572017000100004 ).

For some years now, fisheries management has been immersed in a transition in which the aim is no longer to manage the resource but to manage the users of the resource. The level of profitability has thus become an essential point for decision-making (Dichmont et al. 2010Dichmont C.M., Pascoe S., Kompas T., et al. 2010. On implementing maximum economic yield in commercial fisheries. Proc. Natl. Acad. Sci. U. S. A. 107: 16-21. https://doi.org/10.1073/pnas.0912091107 , Gordon 1954Gordon S. 1954. The Economic Theory of a Common-Property Resource: The Fishery. J. Polit. Econ. 62: 124-142. https://doi.org/10.1021/bi00326a007 , Grafton et al. 2010Grafton R., Kompas T., Chu L., Che N. 2010. Maximum economic yield 273-280. https://doi.org/10.1111/j.1467-8489.2010.00492.x ). Economists have identified that a fishery that maximizes its economic income commonly also satisfies the objectives of conservation and recovery. The development of this scenario, considering the maximization of economic revenue expected from the abalone fishery, allows us to identify a level of effort and catch which is conceptualized as maximum economic yield (MEY) (Clark 1990Clark C.W. 1990. Mathematical Bioeconomics: The Optimal Management of Renewable Resourrces. Nat. Resour. Model. 4: 555-561. https://doi.org/10.1111/j.1939-7445.1990.tb00224.x , Grafton et al. 2010Grafton R., Kompas T., Chu L., Che N. 2010. Maximum economic yield 273-280. https://doi.org/10.1111/j.1467-8489.2010.00492.x ). In most cases this scenario indicates catch and effort levels that are lower than those at MSY, thus generating stock biomass levels higher than MSY. By incorporating these economic analyses, for the first time a management approach that achieves a combination of biological, economic and social objectives can be proposed for the abalone fishery in Mexico.

Unlike other fisheries where strategies that maximize economic rent have been evaluated, although optimality implies that the gains in MEY will more than compensate for the losses in transition, the transition can be burdensome on a fishing industry that is interested mainly in cash flow and short-term returns. (Dichmont et al. 2010Dichmont C.M., Pascoe S., Kompas T., et al. 2010. On implementing maximum economic yield in commercial fisheries. Proc. Natl. Acad. Sci. U. S. A. 107: 16-21. https://doi.org/10.1073/pnas.0912091107 , Kompas et al. 2010Kompas T., Dichmont C.M., Punt A.E. et al. 2010. Maximizing profits and conserving stocks in the Australian Northern Prawn Fishery. Aust. J. Agric. Resour. Econ. 54: 281-299. https://doi.org/10.1111/j.1467-8489.2010.00493.x ). This point alone often makes implementing MEY in fisheries challenging to accomplish. Kell et al. (2006)Kell L.T., Pilling G.M., Kirkwood G.P. et al. 2006. An evaluation of multi-annual management strategies for ICES roundfish stocks. ICES J. Mar. Sci. 63: 12-24. https://doi.org/10.1016/j.icesjms.2005.09.003 suggest that adhering strictly to the precautionary approach for overexploited fisheries may imply setting very conservative (low) effort levels, which may be difficult to accept by fishers and fisheries managers. However, in this case, where there is a TURF allocated to a fishing community with suitable governance and co-management, implementing these strategies and reference points will be easier than in other open-access fisheries or fisheries with participants from different fleets or regions.

Traditionally, TRPs have been defined as a desirable management objective, whereas LRPs indicate a state of a fishery and resource that is considered undesirable and should be avoided (Caddy and Mahon 1995Caddy J.F., Mahon R. 1995. Reference points for fisheries management. Fish. Tech. Pap.). However, we have found no official and public document that explicitly indicates these reference points. Therefore, this study proposes these new bioeconomic reference points.

The Monte Carlo-based simulation analyses also indicate that strategies involving the control of fishing effort can result in lower probabilities of exceeding LRPs. The advantage of incorporating risk and uncertainty in fisheries assessment is that decision-makers in charge of management can have an idea of the potential effect of their decisions. Recognizing the uncertainty present in various parts of the fishery system is fundamental for a precautionary approach to decision-making (Anderson and Seijo 2010Anderson L., Seijo J.C. 2010. Bioeconomics of Fisheries Management. Wiley-Blackwell.).

It is important to add that due to the population dynamics of this stock, which is composed of several substocks, each of which is subjected to periodic (pulse) fishing of high intensity, it is feasible and desirable to analyse the fishery through rotational harvesting schemes based on the proposals of Caddy and Seijo (1998)Caddy J.F., Seijo J.C. 1998. Application of a spatial model to explore rotating harvest strategies for sedentary species. Can. Spec. Publ. Fish. Aquat. Sci. 125: 359-365.. Also, Sluczanowski (1984)Sluczanowski P.R. 1984. A Management Oriented Model of an Abalone Fishery Whose Substocks are Subject to Pulse Fishing. Can. J. Fish. Aquat. Sci. 41: 1008-1014. https://doi.org/10.1139/f84-117 mentions that this type of fishery can be described by a management scheme that is more useful to managers and easier to control in exploitation practice, principally through closure policies, than those based on fishing mortality F.

It seems important that future work consider the possibility of whether spatially explicit management alternatives could be applied in this fishery. As suggested by Caddy and Seijo (1998)Caddy J.F., Seijo J.C. 1998. Application of a spatial model to explore rotating harvest strategies for sedentary species. Can. Spec. Publ. Fish. Aquat. Sci. 125: 359-365. and Seijo and Caddy (2008)Seijo J.C., Caddy J.F. 2008. Port location for inshore fleets affects the sustainability of coastal source-sink resources: Implications for spatial management of metapopulations. Fish. Res. 91: 336-348. https://doi.org/10.1016/j.fishres.2007.12.020 , empirical studies considering spatial management strategies for sedentary species (e.g. spatial rotation harvest schemes) should consider the following set of questions: Do de facto exclusive harvesting rights exist? Is preventing poaching in closed areas/seasons feasible, cost effective and supported by fishers? Is there a management authority with the capacity to allocate fishing rights by area to individual participants? Are there a discrete number of population subunits for the resource? Can the stock be separated into subunits of comparable size, between which migration is limited or absent? Are the number of subunits equal to or greater than a calculated optimum period of harvest rotation? Are there alternative means of employment for local fishers and/or processors if a local resource area is closed for several years? Do fishers have access to other stocks in each year of the scheme? Is the method of harvesting selective for the species and sizes most desired? Considering the above questions, the feasibility of establishing a rotating harvest scheme for the yellow abalone fishery could be explored in the future.

CONCLUSIONS

Three management strategies were evaluated through an SBEM for the yellow abalone fishery in the Mexican North Pacific region in order to determine the risks associated with environmental variability for each of the strategies. By evaluating the state of exploitation of this fishery resource, we identified a biomass recovery strategy that would allow the authorities to reopen the fishery. In addition, reference points were explicitly identified in the fishery to represent bioeconomic management scenarios that allowed us to evaluate alternative management strategies such as minimum effort and effort that maximizes NPV. Calculating the risk of falling below the biological reference points and exceeding the economic reference points provides essential information for decision-making regarding the feasibility of employing any of these management strategies.

Thus, it is concluded that, after the moratorium was established to recover the stocks to the desired levels, the exploitation rate should be lower than the one that was being applied in the status quo, and it was considered suitable to use exploitation rates determined by the E_min and E_maxNPV management strategies. In addition, due to the prevailing environmental variability, there is a risk that the biomass will be below the biological LRP equivalent to 30% in the H. corrugata fishery with the E_msy management strategy (status quo). The risk of achieving a biomass level below the biological LRP is reduced to 0% with the management strategies E_min and E_maxNPV. The E_min and E_maxNPV management strategies exceed the economic LRP and TRP, allowing the economic rent generated by the species and its ecosystem to be increased or maximized while avoiding overexploitation. Future research for fisheries targeting sedentary species under TURF co-management schemes could explore rotational harvest schemes within their spatial management approaches.