ARTICLE

No-take marine reserves can enhance population persistenceand support the fishery of abaloneMarisa Rossetto, Fiorenza Micheli, Andrea Saenz-Arroyo, Jose Antonio Espinoza Montes,and Giulio Alessandro De Leo

Abstract: A critical aspect in the design of a marine reserve (MR) network is its spatial configuration (i.e., the number, size, andspacing of the individual reserves), particularly how these features influence the effect on fisheries. Here, we derived a size-based, spatially explicit, stochastic demographic model to explore how different spatial configurations of MR networks canaffect abundance and commercial yield of the green abalone (Haliotis fulgens), taking as a reference case the abalone fishery of IslaNatividad in Baja California Sur (Mexico). Our analysis suggests that a network of MRs can have a positive effect on abalonepopulation abundance and a slightly negative effect on fishery output with respect to traditional maximum sustainableyield (MSY; i.e., with no reserves). Simulations show that maximum catches achievable with MRs are, under the best configura-tion, �2%–14% lower than traditional MSY depending on the total fraction of the fishing grounds protected. In the case ofoverexploitation, long-term yields can increase following the implementation of MRs. In addition, in the presence of MRs,abundances and yields are much less sensitive to systematic errors in the enforcement of the optimal harvesting rate comparedwith situations in which MRs are not present. Given the limited dispersal ability of the species, the best outcomes in terms offishery output would be achieved with very small reserves — around 100 m wide — so to maximize larval export in the fishableareas. Our results indicate appropriately designed MR networks are an effective strategy for meeting both conservation andeconomic goals under uncertainty. While the size of the existing reserves in Isla Natividad seems adequate to protect the abalonestock, smaller reserves could maximize fishery benefits, although this poses challenges for enforcement.

Résumé : Un aspect clé de la conception d’un réseau de réserves marines (RM) est sa configuration spatiale, soit le nombre, lataille et l’espacement des différentes réserves, en particulier l’influence de ces caractéristiques sur l’incidence du réseau sur lespêches. Nous avons mis au point un modèle démographique stochastique spatialement explicite et basé sur la taille pourexplorer l’incidence de diverses configurations spatiales de réseaux de RM sur l’abondance et le rendement commercial del’haliotide verte (Haliotis fulgens), en utilisant comme scénario de référence la pêche aux haliotides d’Isla Navidad, en Basse-Californie du Sud (Mexique). Notre analyse donne a penser qu’un réseau de RM peut avoir un effet positif sur l’abondance de lapopulation d’haliotides et un effet légèrement négatif sur la production de la pêche par rapport au MSY traditionnel (c.-a-d., sansréserve). Les simulations montrent que les prises maximums possibles en présence de MR sont, dans la meilleure configuration,d’environ 2 % a 14 % inférieures au MSY traditionnel, tout dépendant de la proportion cumulative protégée des zones de pêche.Dans le scénario de surexploitation, les rendements a long terme peuvent augmenter après la mise en place des RM. De plus, enprésence de RM, les abondances et rendements sont beaucoup moins sensibles aux erreurs systématiques dans l’application dutaux de prises optimal par rapport aux situations desquelles les RM sont absentes. Étant donné la faible capacité de dispersionde l’espèce, les meilleurs résultats en termes de production de la pêche pourraient être obtenus avec de très petites réserves —d’environ 100 m de largeur — afin de maximiser l’exportation de larves vers les zones ouvertes a la pêche. Nos résultats indiquentque des réseaux de RM bien conçus constituent une stratégie efficace pour atteindre des objectifs économiques et de conserva-tion dans un contexte d’incertitude. Si la taille des réserves existantes a Isla Navidad semble adéquate pour protéger le stockd’haliotides, de plus petites réserves pourraient maximiser les bénéfices pour la pêche, mais poseraient toutefois des défis en cequi concerne leur application. [Traduit par la Rédaction]

IntroductionIn the past several decades, marine reserves (MRs) have become

a widely advocated approach to marine resource management.The establishment of MRs has been proven to be effective in theprotection of biodiversity and ecosystem structure and function(Leslie et al. 2003; Micheli et al. 2004; Lester et al. 2009). Whenproductive populations are protected within no-take MRs, spill-over of larvae produced in the reserves may also sustain recruit-

ment in the surrounding fishing zones (Roberts et al. 2001; Gelland Roberts 2003), which may increase yields of overexploitedstocks (Holland and Brazee 1996; Sladek-Nowlis and Roberts 1999;Gerber et al. 2003) and contribute to reducing catch variability(Lauck et al. 1998; Mangel 2000). The effects of protection on sus-tainability and yield of populations depends on the spatial config-uration (i.e., on how features such as size of individual reservesand total covering interact with species’ dispersal characteristics).To best accomplish the conservation goal of self-persistence, MRs

Received 3 December 2013. Accepted 20 April 2015.

Paper handled by Associate Editor Marie-Joëlle Rochet.

M. Rossetto. Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, via Ponzio 34/35, I-20123 Milano, Italy.F. Micheli and G.A. De Leo. Stanford University, Hopkins Marine Station, Pacific Grove, CA 93950, USA.A. Saenz-Arroyo. El Colegio de la Frontera Sur (ECOSUR), San Cristobal de las Casas, México.J.A.E. Montes. Sociedad Cooperativa de Produccion Pesquera Buzos y Pescadores, Isla Natividad, Baja California Sur, México.Corresponding author: Marisa Rossetto (e-mail: marisa.rossetto84@gmail.com).

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Can. J. Fish. Aquat. Sci. 72: 1–15 (2015) dx.doi.org/10.1139/cjfas-2013-0623 Published at www.nrcresearchpress.com/cjfas on 8 June 2015.

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should be large enough relative to the dispersal distance of thetarget species to ensure sufficient larval retention (Botsford et al.2001; Kaplan et al. 2006). On the other hand, maintaining highyields in fisheries may require a more sophisticated spatial con-figuration; in fact, a fishery-effective network of MRs requires thatthe size of, and space between, marine reserves is designed so thatreproductive output within no-take areas can contribute throughspillover to recruitment outside MRs (i.e., in the still fishableground; Halpern and Warner 2003; Hastings and Botsford 2003;Neubert 2003; Gaines et al. 2010).

Abalones (Haliotis spp.) are large benthic mollusks that havebeen intensely fished worldwide, and stocks are currently de-pleted in most countries (Shepherd et al. 1998a; Karpov et al. 2000;Dichmont et al. 2000). The implementation of MRs is receivinggrowing attention as a promising tool for protecting and possiblyrecovering abalone stocks. Empirical work on the effect of MRs onHaliotis spp. confirms the expectation that sedentary species withdispersal in the larval phase and a history of overexploitationmight benefit from the implementation of MRs (Hastings andBotsford 1999; Botsford et al. 2003). Inside MRs, significantlygreater densities (up to ten times) relative to unprotected siteshave been reported for several Haliotis species (Wallace 1999;Maliao et al. 2004; Parnell et al. 2005). In addition, inside reservesabalones attain bigger size than abalones in fished areas (Edgarand Barrett 1999; Wallace 1999; Parnell et al. 2005; Maliao et al.2004; Micheli et al. 2008, 2012). Finally, within the boundaries ofprotected areas, abalones are more likely to be found in aggrega-tions relative to exploited sites (Parnell et al. 2005). As abalonefecundity increases with individual size (Tutschulte 1976) and fer-tilization success is enhanced when abalones are found in highdensities (Button and Rogers-Bennett 2011), combined responsesof abalone densities and size structure to protection can augmentthe reproductive output of protected populations (Micheli et al.2012). The enhanced production of larvae could, in turn, sustainrecruitment in the surrounding fished areas if MRs are properlydesigned to allow the export of larvae beyond the reserve bound-aries (Micheli et al. 2012). Recent modeling work on the conserva-tion and economic effectiveness of proposed networks of MRs incentral California indicates that for Haliotis rufescens, small pro-tected areas can support population persistence inside theirboundaries, and conservation benefits increase with increasingtotal reserve coverage (White et al. 2010, 2011). The model of Whiteet al. (2010, 2011) indicates that MRs could increase abalone yieldswhen the resource is heavily fished, but given the species’ shortdispersal ability, the expected catches under the proposed net-work configurations were substantially lower than the theoreticalmaximum sustainable yield (MSY) (White et al. 2010, 2011).

The goal of the present work is to investigate under whichspatial arrangement — in terms of size of individual reserves andtotal closed area — MRs can be part of the optimal management ofabalone fisheries (i.e., to assess whether a properly designed net-work of MRs can foster the recovery of overexploited populationsand, at the same time, sustain fishery output). To address thisquestion we developed a size-structured demographic model ofgreen abalone (Haliotis fulgens) and used it to explore alternativescenarios of MR implementation. While our model structure isgeneral, we performed the analysis taking inspiration from thegreen abalone fishery of Isla Natividad, Baja California Sur,Mexico, where two MRs have been recently established with theaim of protecting remaining populations of abalone, allowingfor their recovery and enhancing fishery yields. In the BajaCalifornia peninsula, the fishery of Haliotis corrugata and H. fulgensis still a valuable business; however, current catch levels of bothspecies remain far below the historical landings in the middle of the

past century, and great concern exists regarding the sustainability ofthe fishery (Ponce-Díaz et al. 1998; Morales-Bojórquez et al. 2008). Asother fishing communities in Baja California are establishing similarMRs (so far at two additional locations; F. Micheli and A. Saenz-Arroyo, unpublished data), it is crucial to explore under what reservenetwork configurations larval spillover from the protected areasmay enhance abalone population persistence and possibly supportfishery yield.

Materials and methodsWe developed a size-structured, spatially explicit demographic

model for H. fulgens to explore the possible effect of MR implemen-tation on abalone population and fishery yields. The demographicmodel was developed with reference to the green abalone fisheryoperating since the 1940s in Isla Natividad, a small island on thePacific coast of Baja California Sur (Mexico). A detailed descriptionof this fishery is presented in the section on The abalone fishery ofIsla Natividad.

The model incorporates quantitative information on abalonegrowth, size-dependent mortality, size-dependent fecundity, lar-val and settler survival, and dispersal in the larval phase, as de-scribed in the sections on Model description and Parameter valuesand specific formulation. We used the demographic model toexplore how different combinations of fishing harvest and MRnetwork configuration might influence (i) abalone populationpersistence in terms of long-term abundance and (ii) long-termfishery yields, as detailed in the section on Decision variables,scenarios, and model simulations. Elasticity and sensitivity anal-yses (see section below) were carried out to evaluate the impor-tance of vital rates and the effect of uncertainty in demographicparameters on model outputs.

The abalone fishery of Isla NatividadIsla Natividad is representative of the 22 fishing cooperatives

operating in the Baja California peninsula targeting green (H. fulgens)and pink abalone (H. corrugata) (Ponce-Díaz et al. 1998). The manage-ment of abalone fishery on the island is based primarily on exclu-sive access granted for 20-year periods by the Mexican federalgovernment, in addition to minimum landing sizes (MLS) andannual quotas for the target species. The MLS in Isla Natividad forH. fulgens is 155 mm in shell length (SL). In the past decades, annualquotas have been set at as much as 30% of the estimated commer-cial stock biomass of animals above the MLS (Shepherd et al.1998a). Control of fishing effort is well enforced, and poaching isvirtually absent thanks to the exclusive access privileges andthe geographical isolation. However, errors in stock assessmentcan lead to overestimation of population densities, and there-fore, actual harvest rates may exceed the target. Catches werehigh in the period 1965–1990, with a maximum harvest of140 t·year−1 registered in the early 1970s; from 1990, green ab-alone harvests on the island have declined, remaining below20 t·year−1 in the last decade (see online Supplementary mate-rial, Fig. S11). The fishing ground of the island stretches more orless uniformly around the �15 km island perimeter and up to500 m from the coast (Fig. 1), covering an area of about 750 hect-ares (ha). To facilitate management, abalone fishing groundsof Isla Natividad are divided into blocks of 500 m × 500 m, apractice also in place in other abalone cooperatives along BajaCalifornia (Rodríguez-Valencia et al. 2004; Morales-Bojórquezet al. 2008). In 2006, two no-take MRs, 500 and 1000 m wide, wereestablished on Isla Natividad, covering �8% of the fishing grounds(Fig. 1).

1Supplementary data are available with the article through the journal Web site at http://nrcresearchpress.com/doi/suppl/10.1139/cjfas-2013-0623.

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Model descriptionThe fishing ground was schematically modeled as a closed cir-

cular belt of 150 contiguous patches of 100 m width, extending500 m from the coastline, with the first and last patch beingconnected as in a torus. All patches were assumed to be equallysuitable for abalone so that the demographic processes character-izing abalone life cycle were identical in each patch. Although it ispossible that some patches could support higher growth rates orcarrying capacity owing to local favorable conditions of foodand (or) habitat, no data were available to this regard; therefore,we simulated a homogeneous habitat without incorporating spa-tial patterns in abalone’s life traits.

The demographic model described yearly changes in the popu-lation abundance of green abalone in each patch as resulting from(i) reproduction and planktonic larval dispersal; (ii) harvesting;(iii) natural mortality; and (iv) somatic growth. What differenti-ated one patch from another was whether the patch was exploited

at a harvesting rate h or whether it was set aside as no-take reserve(h = 0).

The structure of abalone population in each patch was rep-resented by nine size classes of 25 mm width: three juvenileclasses (5–30, 30–55, 55–80 mm) below the size at first repro-duction (i.e., �80 mm; Shepherd et al. 1991); three classes in-cluding unfished adults (80–105, 105–130, 130–155 mm); andthree classes including fished individuals (155–180, 180–205,205–230 mm), whose sizes are comprised between the MLS andthe maximum size of green abalone registered in Baja Califor-nia (�230 mm; Rossetto et al. 2013; Rodríguez-Valencia et al. 2004).Accordingly, the state variables of the model were Ni,z,t (i.e., the aba-lone density (individuals·ha−1) in size class i, patch z at time t. Thebasic dynamic equation is

(1) Nz,t�1 � MtNz,t � Rz,t

Fig. 1. Location of Isla Natividad, Baja California Sur, Mexico. The fishing grounds are divided into blocks (�500 m × 500 m); dark grey blocksrepresent the two marine reserves currently established on the island.

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where Nz,t = [N1,z,t,N2,z,t,…,N9,z,t]T is the vector of popula-tion densities in each size class at time t in patch z, M is a9 × 9 transition matrix (Caswell 2001) including growth, adult

survival, and harvest, and R = [Rz,t,0,0..0]T is the recruitmentvector.

Matrix M takes the following form:

(2) �g1,1s1 0 0 0 0 0 0 0 0g1,2s1 g2,2s2 0 0 0 0 0 0 0g1,3s1 g2,3s2 g3,3s3 0 0 0 0 0 0g1,4s1 g2,4s2 g3,4s3 g4,4s4 0 0 0 0 0g1,5s1 g2,5s2 g3,5s3 g4,5s4 g5,5s5 0 0 0 0g1,6s1 g2,6s2 g3,6s3 g4,6s4 g5,6s5 g6,6s6 0 0 0g1,7s1 g2,7s2 g3,7s3 g4,7s4 g5,7s5 g6,7s6 g7,7s7 (1 � h) 0 0g1,8s1 g2,8s2 g3,8s3 g4,8s4 g5,8s5 g6,8s6 g7,8s7 (1 � h) g8,8s8 (1 � h) 0g1,9s1 g2,9s2 g3,9s3 g4,9s4 g5,9s5 g6,9s6 g7,9s7 (1 � h) g8,9s8 (1 � h) s9 (1 � h)

�where gi,j is the probability of individuals of class i to growth toclass j the following year, si is the size-dependent fraction of indi-viduals in class i in a given year that survive to the following year,and ht is the fraction of individuals yearly harvested by fishermenin year t.

The number of eggs produced in each patch z at time t wascalculated as follows:

(3) Ez,t � �i

0.5ewi�iNi,z,t

where e is the number of eggs per unit mass (g−1) produced by agreen abalone female; wi is the mass (g) of abalone in size class i;�i is the fraction of sexually mature individuals of class i; and thefactor 0.5 accounts for a 1:1 sex ratio.

Our model assumes dispersal in the larval stage; therefore, fer-tilized eggs successfully developing in larvae were assumed to bepartially retained in the source patch and partially exported tocontiguous patches. In particular, probability of dispersal at dis-tance x (m) from the center of the patch was described by a Gauss-ian distribution, namely

(4) p(x, t) �1

�2��d2(t)

e

x2

2�d2(t)

with standard deviation �d(t) set so that 99% of larvae are retainedat a distance ±d(t) from the source. The fraction of larvae � dispers-ing k patches away from the source patch, with k = ±1, ±2, …, washence computed as follows:

(5) �(k) � �100�k�

1

2�

100�k�1

2�

1

�2��d2(t)

e�

x2

2�d2(t)dx

where “100” in the integration interval is the size of any of the150 patches representing the coastline. Accordingly, �(0) is theretention rate (i.e., the fraction of locally produced larvae thatremains in the source patch).

The number of settlers in patch z at time t was calculated sum-ming the contribution of all patches j as follows:

(6) Sz,t � �E�J

Ej,t�(|j � z|)

where J is the set of patches, and �E represents the survival fromeggs to settlers, which accounts also for the fertilization success.

Recruitment in patch z at time t was assumed to be equal tonumber of settlers S in patch z at time t that survive to the first sizeclass:

(7) Rz,t � �S Sz,t

with �S being the survival of settlers.Total yearly catch on the island in biomass (t) was computed as

follows:

(8) Ct � 106�Zf

A�If

wi ht Ni,z,t

where A is the area of each patch (5 ha), Zf is the set of fishablepatches (i.e., those that are not set aside as no-take zone), If iden-tifies the size classes above MLS, and ht is the fraction of commer-cial size abalone that are harvested from each fishable patch inyear t.

Model variables and parameters are summarized in Table 1, anda detailed description of specific model equations and parametersis presented below.

Parameter values and specific formulation

Body massBody mass wi (g) was computed from mean shell length li of an

individual in class i (mm) using the length–mass relationship forgreen abalone reported in Shepherd et al. (1998a):

(9) wi � 2.24 × 10�5 li3.36

Natural mortality in adultsIn abalone, natural mortality rates of settled individuals have

been shown to be size-dependent, with survival probabilities in-creasing with size (Rossetto et al. 2012). Accordingly, size-specificmortality rates i (year−1) were calculated from mean body mass ineach size class wi (g) using the empirical allometric relationshipbetween instantaneous mortality rates and body mass reportedfor abalones in natural environments (Rossetto et al. 2012):

(10) ln i � � � · ln wi

where � was assumed to be −0.317 (SD = 0.027), and was 0.635(SD = 0.102). These are the estimated means and standard devia-tions of the parameters of the log–log relationship obtained forH. fulgens, as in Rossetto et al. (2012). Annual survival si (i.e., the

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fraction of individuals in class i that survive to the following year)was then computed as

(11) si � e�i

Somatic growthGrowth transitions represent the fractions of individuals in a

given class that remain in the same size class or grow to the followingones after a year. To model the somatic growth of H. fulgens,we assembled a dataset of 53 observations consisting of annualgrowth rates in shell length registered in the field and in labora-tory conditions. Specifically, we retrieved growth data from tag-ging experiments conducted in Bahía Tortugas and in BahíaAsunción (Baja California Sur, Mexico) by Shepherd et al. (1991)and by Guzmán del Próo and Lopez-Salas (1993) and from labora-tory experiments by McCormick et al. (1992), Aviles and Shepherd(1996), and Durazo-Beltrán et al. (2003). Laboratory data were in-

cluded as they provide information on the growth of juveniles,not represented in the field samples. A summary of the data re-porting the range of size at capture, time at liberty, and lengthincrement is reported in Table 2. To estimate growth transitionsfrom green abalone mark–recapture data, we used a probabilisticGompertz model for non-negative growth, developed by Bardos(2005) to describe the somatic growth of another abalone species(Haliotis rubra), which consists of a probability distribution of sizeincrements given the size at capture in which the asymptoticlength is conditional on the initial length. The somatic growthmodel, described in more detail in Appendix A, included threebiologically significant parameters — the growth parameter G,the mean asymptotic length Ln, and its variance �L

2 — and twoadditional, phenomenological parameters, � and (Bardos 2005).The model was fitted to the tag–recapture data using maximumlikelihood estimation. The estimated growth parameters were

Table 1. Parameters and variables of the demographic model for Haliotis fulgens.

Symbol Description (units and values when applicable) Equation

Index and spatial variablest Time index (year) 1i Size class index 1z Patch index 1If Set of size classes above minimum landing sizes (MLS) 3Zf Set of fishable patches 3A Patch area (5 ha) 3Ni,z,t Abalone density in size class i, patch z, at time t (individuals·ha−1) 1, 3, 8Ez,t Number of eggs produced in patch z at time t (eggs·ha−1) 3, 6Sz,t Number of settlers arriving in patch z at time t (individuals·ha−1) 6, 7, 12Rz,t Number of new recruits in patch z at time t (individuals·ha−1) 1, 7

HarvestMLS Minimum landing size in shell length (155 mm) —h Fraction of commercial size abalone that are harvested from each fishable patch 2, 8Cw,t Total yearly catch on the island in year t (tonnes) 8

Length and masswi Mean body mass of individuals of class i (g) 3, 8, 9, 10li Mean shell length of individuals of class i (mm) 9

Natural mortalityi Instantaneous annual mortality rate of individuals in class i (year−1) 10, 11si Fraction of individuals in class i that survive from year t to year t + 1 2, 11 Intercept of the allometric relationship between instantaneous mortality rates and

body mass (mean = 0.631, SD = 0.102)10

� Slope of the allometric relationship between instantaneous mortality rates andbody mass (mean = −0.371, SD = 0.027)

10

Somatic growthgi,j Growth transition from class i to class j 2, A6G Growth parameter of the probabilistic Gompertz growth curve (year−1) A1, A2Ln Mean asymptotic length (mm) A3, A4�L

2 Variance of the mean asymptotic length (mm2) A3, A4� Phenomenological parameter of the probabilistic Gompertz growth curve A3, A4 Phenomenological parameter of the probabilistic Gompertz growth curve A3, A4

Fecunditye Number of eggs produced per gram of individual (eggs·g−1) (mean = 3772, SD = 330) 3�i Fraction of sexually mature individuals of class i 3

Larval and settler survival�E Survival from eggs to settlers (mean = 3.09×10−3, SD = 0.33×10−3) 6�S Survival of settlers during the first year of life 12�0 Survival of settlers at low densities (0.01) 7, 12K Carrying capacity of settlers (107 individuals·ha−1) 12

Larval dispersald Larval dispersal distance (m); variable according to a gamma distribution with

maximum probability of dispersal around 1000 m—

p(x,t) Probability of dispersal at distance x (m) from the center of the patch 4�(k) Fraction of larvae dispersing k patches away from the source patch 5, 6

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then used with eq. A6 in Appendix A to derive the transitionelements gi,j (i.e., the fraction of individuals in size class i in year tthat grow into class j the following year).

FecundityThe number of eggs e (g−1) produced by a green abalone female

was assumed to be equal to 3772 with a standard deviation of 330(Tutschulte 1976). �i (i.e., the fraction of sexually mature individu-als of class i) was assumed to be a sigmoidal increasing function ofsize li, as described in Rossetto et al. (2013).

Larvae and settlers survivalThe survival from eggs to settlers �E was assumed to be equal to

3.09 × 10−3 (SD = 0.33 × 10−3) as estimated by Rossetto et al. (2013) onstock–recruitment data from Isla Natividad.

The survival of settlers during the first period of life can benegatively affected by settler density because of competition forfood, space, or refuges (Connell 1985; McShane 1992). Indeed,density-dependent survival in the postsettlement phase has beenobserved for several Haliotis species, both in laboratory (Daumeet al. 2004; Day et al. 2004) and natural conditions (McShane 1991;Shepherd et al. 1998b), with instantaneous mortality of settlersincreasing linearly with settlers’ density (Shepherd 1990). Accord-ingly, recruitment was modeled as a Ricker function with settlers’survival (�S) being a negative exponential function of their den-sity:

(12) �S � �0e�Sz,t/K

where �0 represents the survival of settlers in low-density condi-tions, and K is a measure of carrying capacity (Sladek-Nowlis andRoberts 1999). Direct measures of postlarval survival during thefirst year of life are not available for H. fulgens in the naturalenvironment. However, experimental studies conducted in thewild for several abalone species (Shepherd et al. 1998b) suggest aninstantaneous mortality rate of about 2 (months−1) in the firstmonth of life and 0.2 (months−1) from 2 to 12 months at low-density conditions. By integrating these settler mortality ratesover the year, we assumed a value of �0 of the order of 1%. Thevalue of K was assumed to be 107 individuals·ha−1, given the highmortality rates observed at postlarvae densities above this thresh-old (�1000 individuals·m−2; McShane 1991; Daume et al. 2004).

Abalone larval dispersalAvailable studies suggest that abalone larvae — which spend

5–10 days in the water column before attaching to the substratum(Guzmán del Próo et al. 2000) — are mostly retained in areas closeto parental reefs, because of the short larval duration and becauseextensive kelp beds and small-scale eddies substantially attenuatethe larval flux (Shepherd et al. 1992; Guzmán del Próo et al. 2000).A majority of studies indicates that abalone larval dispersal dis-tance is limited to hundreds of metres (Prince et al. 1988; McShaneet al. 1988; Shepherd et al. 1992; Guzmán del Próo et al. 2000;Shanks et al. 2003; Temby et al. 2007). However, strong currents orstorms may occasionally drive abalone larvae several kilometres

away (Tegner and Butler 1985; Sasaki and Shepherd 1995). In IslaNatividad, an experimental study on abalone larvae spillover sug-gested dispersal distances of �300 m (Micheli et al. 2012). In thepresent study, we assumed that the larval dispersal distance d(t) ofabalone varies stochastically from year to year according to agamma distribution with shape = 3 and rate = 0.007 (Fig. S21). Thisright-skewed distribution has a mode around 300 m and assumesthat dispersal on the scale of hundreds of metres is more plausiblethan dispersal over longer distances (>1 km).

Decision variables, scenarios, and model simulations

Reserve effect on long-term abalone abundance and yieldWe used the model to explore the effects on stock and fisheries

yield of a combination of different levels of harvest rates h (frac-tion of abalones over MLS removed each year from the patchesopen to fishing), protection level (PL, the overall share of fishingground set aside in no-take reserves), and size (m) of the individualreserves in the MR network. Mean harvest rate ranged between 0and 0.9; PL was set to 0% (no reserve), 10%, 20%, 30%, 40%, or 50% ofthe overall fishing ground; size of individual reserves was 100, 500(the actual size of the existing no-takes zones in Isla de Natividad),or 1500 m, with the first and the last size being smaller andgreater, respectively, than the mean dispersal distance of abalonelarvae. Individual reserves were assumed to be uniformly spacedalong the coastline so as to cover the assigned PL of the fishingground; an example of a 30% PL achieved with no-take areas ofdifferent sizes is depicted in Fig. 2, and the number of protectedareas for each combination of PL and size is reported in Table 3.Each combination of the harvest rate, PL, and individual reservesize identified a management scenario.

To initialize the model, we reproduced the plausible exploita-tion history of green abalone (see Shepherd et al. 1998a) by simu-lating 50 years of fishing in which 30% of individuals above theMLS are removed each year in each patch. The resulting popula-tion abundance and structure was used as initial conditions foreach management scenario. To account for year-to-year variabilityin larval dispersal, we used Monte Carlo simulations and ran-domly drew the value of d (dispersal distance) at each time stepfrom the gamma distribution as explained in the section on Modeldescription. Fishery performance and stock size for each scenariowere analyzed over 150 years, a time frame that was sufficient toreach stochastic stationarity. For each scenario we replicated sim-ulations a large number of times and used the correspondingoutput to compute mean and standard deviations of stock abun-dance and fishery yield. Preliminary tests showed that both meansand standard deviations of model outputs were already stableafter 100 replicates, and the confidence intervals remained sub-stantially constant for the number of replicates ranging between1000 and 10 000; therefore, we set the number of replicates to1000, as this appeared to be a reasonable choice to derive robuststatistics without excessively increasing computing time. All sim-ulations were run using R (version 3.1.0).

Table 2. Summary of growth data used for estimation of growth transitions of H. fulgens.

Source N LocationInitiallength (mm)

Time atliberty–rearing(years)

Lengthincrement(mm·year−1)

Shepherd et al. 1991 32 Bahía Tortugas 59.4–140.3 1 11–43.6Guzmán del Próo and

Lopez-Salas 199313 Bahía Asunción 68–143 0.98 13–50

Durazo-Beltrán et al. 2003 3 Laboratory 5.7–6.1 0.9 14.6–15.9Aviles and Shepherd 1996 1 Ocean barrel culture 14.8 0.9 16.3McCormick et al. 1992 4 Land and ocean culture 35.5 0.73 19.1–21.9

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Elasticity and sensitivity analysesSensitivity analyses are crucial to determine which parameters

are most influential on model results and how uncertainty prop-agates on model outputs. In classical population matrix models ofthe form Nz,t+1 = AtNz,t, sensitivity is defined as the partial deriva-tive of a population’s finite growth rate (�) to changes in theprojection matrix elements (aij) (Caswell 2001). Elasticities (i.e.,proportional sensitivities) are frequently used instead of sensitiv-

ity to account for the different scales of each matrix element andare defined as

ei,j �ai,j

����ai,j

Here, we rewrote eq. 1 in the form Nz,t+1 = AtNz,t, and followingthe approach of Caswell et al. (2004) for models with density de-pendence, we evaluated elasticities of the projection matrix at thelong-term equilibrium, when � = 1, in the absence of fishing andunder the scenario of no MRs.

Additionally, we assess how uncertainty in the estimation ofdemographic parameters affects long-term population abun-dances and yields following the approach proposed by McCarthyet al. (1995). Specifically, we were interested to assess model sen-sitivity to highly uncertain parameters (i.e., mortality parameters( and �), eggs produced per gram of individual (e) and survivalfrom eggs to settlers (�E)). We proceeded as follows:

(i) A set of model parameters was randomly sampled from nor-mal distributions defined according to the mean and standarddeviation of their estimates (see Table 1).

Fig. 2. Example of three alternative spatial arrangements of marine reserves to achieve an overall protection of 30% of the fishing groundson an island coastline divided in 150 patches. Shaded areas indicated protected blocks, while white areas indicated fished blocks. A30% protection of the fishing grounds could be achieved with networks of 45 no-take zones of 100 m, 9 zones of 500 m, or 3 zones of 1500 m.The larval dispersal kernel corresponding to d = 300 m is also depicted. For sake of simplicity, the coastline around the island is depicted as alinear array, although in the model the first and the last patches are connected (see Materials and methods).

0 5000 m 10000 m 15000 m

Reserve size: 100 m

Number of reserves: 45

0 5000 m 10000 m 15000 m

Reserve size: 500 m

Number of reserves: 9

0 5000 m 10000 m 15000 m

Reserve size: 1500 m

Number of reserves: 3

Table 3. Number of individual reserves along the 15 km long coastlineof Isla Natividad for each combination of protection level and reservesize used in the analysis.

Protectionlevel (% groundin MRs)

No. of smallreserves(100 m)

No. ofintermediatereserves (500 m)

No. of largereserves(1500 m)

10% 15 3 120% 30 6 230% 45 9 340% 60 12 450% 75 15 5

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(ii) A simulation of 150 years each was run by keeping the modelparameters drawn at point (i) fixed for the entire simulation time.For each simulation, we retained the value of long-term popula-tion abundance and yield (at time t = 150).

(iii) We went back to point (i), randomly drew a new set of modelparameters, and replicated the process 100 times.

Sensitivity was assessed for the scenario with no MR (PL = 0) andover harvest rates from h = 0 to h = 0.9. We explored the relation-ship between the 100 values of model parameters (independentvariables) drawn at point (i) and the values of population size andlong-term yield (response variables) using multiple ordinary re-gression with normal error structure, using the “src” function of Rpackage “Sensitivity” (version 3.1.0). The relative importance ofeach model parameter was indicated by its standardized regres-sion coefficient, that is, the coefficient value divided by its stan-dard error (Cross and Beissinger 2001). The absolute value of thestandardized regression coefficient represents the importance ofthe parameter in determining the status of the population, whilethe sign represents the direction of the contribution. For each setof random parameters, we also retrieved the harvest rates thatmaximize catches to evaluate their sensitivity to parameter un-certainty.

Results

Somatic growthThe maximum-likelihood estimation of the Gompertz model

on length-increment data provides G = 0.56 ± 0.10 year−1, Ln =150.39 ± 49.29 mm, �L

2 = 55.96 ± 28.67 mm2, � = 1.47 ± 0.63, and =1.52 ± 0.85. The Gompertz model fitted to mark–recapture dataprovides length increments that closely resemble the observeddata (Fig. 3a). The growth model efficiently captures the highgrowth variability of the small size classes and the accelera-tion of growth rates of the juvenile stages, which can exceed50 mm·year−1 (Fig. 3a). Although tagged individuals were all below150 mm SL (Fig. 3a), the model predicts a growth trajectory even-tually approaching �250 mm (Fig. 3b), which is consistent withmaximum sizes of green abalone observed in California (Parnellet al. 2005). The growth model indicates that H. fulgens reaches thesize of sexual maturity (136 mm SL) at an age between 4 and5 years and enters the fishery (155 mm SL) at an age between 5 and7 years.

Model evaluationThe model predicted that under pristine conditions, densities

of individuals >10 cm SL — those generally sampled by underwa-

ter visual censuses (Parnell et al. 2005; Rossetto et al. 2013) — were2456 individuals·ha−1, a value comparable to baseline abundancesand unfished densities estimated for several Californian abalones(Rogers-Bennett et al. 2002; Micheli et al. 2008). After 50 years offishing at h = 0.3, the model predicted that densities of abalonesabove 10 cm were reduced to 410 individuals·ha−1. In the absenceof MRs (i.e., under the hypothesis of spatially homogeneous fish-ing effort), long-term abundances and yields were insensitive tothe magnitude and variability of abalone dispersal distance. Esti-mates of H. fulgens densities at Isla Natividad in 2008–2009 infished sites ranged from 62 ± 164 to 135 ± 260 individuals·ha−1

(Rossetto et al. 2013). Our model results for abalone densities afterexploitation were higher than observed values, but they wereclose to the upper range of the field estimates. The model pre-dicted that fishing at h = 0.3 for 50 years would initially deliver amaximum catch from the entire island of 149 t·year−1 that gradu-ally decreased to 12 t·year−1 (mean over 50 years: 32 t·year−1). Thesefigures are comparable to real catch data recorded in Isla Nativi-dad, where, in the past decades, yearly catches reached a maxi-mum of 143 t in 1973 and declined to 10 t·year−1 in 2008, with amean value over 50 years of 53 t·year−1 (Fig. 1).

Reserve effect on long-term abundanceIn the absence of MRs, the harvest rate in each patch needed to

be substantially smaller than 0.3 to prevent abalone populationabundance to drop below 4 million individuals (i.e., �10% of itsundisturbed level of approximately 32 million individuals; Fig. 4d,Fig. S31). Establishment of MRs had a positive effect on the greenabalone population of Isla Natividad by offering protection to afraction of the stock; the larger the PL, the greater the long-termabalone population size (Fig. 4, Fig. S31). Long-term populationabundance depended on the combination of harvest rate and PL;the larger the harvest rates in the fishable patches, the larger thefraction of habitat that needed to be protected to prevent popula-tion decline (Fig. 4, Fig. S31). However, when reserves coveredmore than 40% of the habitat, mean abalone abundance neverdropped below 15 million individuals (almost half of its undis-turbed conditions) for any level of harvest rate applied outsideMRs (Fig. 4f). Under current management (h = 0.3, PL = 10%),abalone population was predicted to stabilize around 9.26 ±0.43 million individuals, corresponding to 28% of the undisturbedconditions (Fig. 4b, Fig. S31).

Overall, mean long-term abalone stock size tended to be greaterwith small or medium reserves (i.e., 100 and 500 m; Fig. 4) thanwith larger reserves (i.e., 1500 m), except for the combinations ofhigh harvest rates and low PL (Figs. 4c, 4e).

Fig. 3. Predictions of the probabilistic Gompertz growth curve fitted on green abalone length-increment data. (a) Comparison betweenobserved and simulated length increments �l (mm) versus initial length l1 (mm). Larger black dots are observed length increments (seeTable 2). Small points are the result of 20 stochastic simulations of the Gompertz growth curve. (b) Predicted size-at-age based on 20 stochasticsimulations of length increments, assuming that individuals are 1 mm shell length at age zero.

0 50 100 150

0

10

20

30

40

50

60

l1 (mm)

Δl

(mm

y−1

)

a

0 5 10 15

0

50

100

150

200

250

age (y)

l age

(m

m)

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Fig. 4. Long-term abalone abundance for the whole island (millions of individuals, mean ± SD of the 1000 replicates under the assumption of year-to-year variability in larval dispersaldistance) as a function of protection level (a–c) and harvest rate (d–f) for small reserves of 100 m width (black symbols), intermediate reserves of 500 m width (gray symbols), or withnetworks of large reserves of 1500 m width (white symbols).

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05

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Long

−te

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bund

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(x1

06 ind) h=0.1

a

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(x1

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b

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(x1

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c

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Variability in model output due to the assumed year-to-yearvariation in dispersal distance was limited and appeared to beslightly greater for intermediate reserve size (Fig. 4). Mean coeffi-cients of variation of long-term abundances were 3.09%, 3.99%,and 2.97% for small, intermediate, and large reserves, respectively.

Reserve effect on long-term fishery yieldIn the absence of reserves (PL = 0), the maximum long-term

yield (or MSY) stabilized at 25 t of fresh mass (without shell) peryear, and the corresponding mean harvest rate (hMSY) was equal to0.1 of abalones above the 155 mm MLS (Fig. 5d, Fig. S41). When MRswere present, the mean long-term yields were determined by thecombination of PL and the harvest rates in the fished patches.When harvest rates in the fishable patches were maintainedat sustainable levels (h 0.1), expanding the reserve networkentailed a reduction of fishery yields compared with traditionalmanagement (Fig. 5a). On the contrary, when harvest rates in thefishable areas exceeded the sustainable ones, increasing PL couldhave a positive effect on fishery yields (Figs. 5b–5c). The relation-ship between the mean long-term fishery yield and the harvestrate h was unimodal but with substantial differences dependingupon the PL (Fig. 5, lower panels); in the absence of MRs, theyield–h relationship was characterized by a very narrow pickaround h 0.1, with the yield sharply declining to very low valuesfor harvest rates above 0.2 (Fig. 5a). In the presence of MRs cover-ing a limited fraction of the grounds such as a 10% closure, theshape of the relationship between fishing mortality and fisheryyields was similar to that in the absence of MR (Fig. 5e). On thecontrary, for PL equal to 30% or larger, the yield–h relationshipremained high and remarkably flatter at the right side of thecurve, providing high yields for a wide range of harvesting rates(Fig. 5f). In general, small reserves sizes (100 m) had better fisheryperformances than intermediate (500 m) or large (1500 m) reservesizes (Figs. 5, Fig. S41). In scenarios with small reserves, however,yield was predicted to be low under low PL and high harvest rates(Figs. 5c, 5e). In scenarios with large reserves, sustainable yield wassubstantially lower than MSY, although less sensitive to changesin h and in PL. We calculated that with the current extension ofMRs (PL = 10%, h = 0.3), the maximum yield could not exceed 9.6 ±0.5 t·year−1 (Fig. 5, Fig. S41). Year-to-year variation in yield resultingfrom variability in dispersal distance appeared to be limited andslightly greater for intermediate reserve size (Fig. 5), with meancoefficients of variation on long-term yields being 4.07%, 8.84%,and 7.05% for small, intermediate, and large reserves, respectively.

Maximum catches achievable with networks of small reserveswere 2%–14% lower than MSY under optimal traditional manage-ment depending on the total fraction of the fishing grounds pro-tected (Fig. 6). With medium and large reserves, maximum yieldswere between 8% and 27% and between 9% and 44% lower thanMSY in absence of reserves, respectively (Fig. 6). Optimal manage-ment with a network of MRs generally requires harvesting rate tobe larger than the harvest rate providing MSY under traditionalmanagement (Fig. 6).

Elasticity and sensitivity analysesThe elasticity analysis of the green abalone projection matrix

suggests that the population at the long-term equilibrium is mostsensitive to survival in the largest size class (205–230 mm; Fig. S51),reflecting the fact that fecundity increases with body size in aba-lone, and thus the largest abalones are the most important spawn-ers. All the coefficients on the main diagonal of the projectionmatrix are characterized by high elasticity as well as the coeffi-cient of the first row corresponding to the product of fecundityand settlement survival.

The sensitivity analysis performed over a wide range of varia-tion of the parameters of the size-dependent mortality function,settlement survival, and fecundity showed that across all harvestrates scenarios, the demographic parameters that most affect

both population size and catches were mortality parameters and� (Fig. 7). Specifically, an increase in (entailing an increase inmortality of all size classes) and � (entailing an increase in mor-tality of adults) reduces both the stock and the long-term yield.Conversely, an increase in egg per unit mass (e) and survival fromegg to larvae (�E) positively affected both population size andcatches. However, their effect was negligible, as the recruitment(the actual number of settlers recruiting each year) was modu-lated by the demographic bottleneck provided by the density-dependent survival. Overall, simultaneously accounting forparameter uncertainties translated to a high variability in modeloutputs, with mean coefficients of variation up to 138% and 188%for abundances and catches, respectively. Importantly, the har-vest rates predicted to maximize catches (hMSY) were quite robustto parameter uncertainty, remaining equal to 0.1 for 56% of cases,0.2 for 36% of cases, and 0.3 for 8% of cases.

DiscussionOur modeling analysis shows that an appropriately designed

MR network can meet both conservation and economic goals inthe management of the green abalone fishery. In particular, ourresults suggest that a network of MRs can increase populationabundance and make the system more robust to errors in thedetermination and enforcement of catch limits, while entailingonly minor losses in yields comparable to MSY under traditionalmanagement (e.g., Hastings and Botsford 1999). Thus, MR net-works can be part of management strategies aimed at maintain-ing abalone catches while addressing unavoidable uncertaintiesin the management system and the environment.

Our model suggests that the implementation of MRs network isexpected to have a positive effect on abalone population persistence,providing an effective tool for augmenting the abundance of thestock. The modeling results indicate that, for abalone, conservationbenefits are maximized for medium reserves (500 m wide), which arepredicted to ensure high long-term population abundance and anegligible risk of collapse even when harvest rates in the remainingfishing areas are intensive. The predicted positive effect of protectionin preserving high abalone population abundance is consistent withempirical studies of existing MRs conducted on several species of thegenus Haliotis (Wallace 1999; Maliao et al. 2004; Parnell et al. 2005)and on other marine species (Roberts et al. 2001; Micheli et al. 2004).Our results are also in agreement with analytical solutions of math-ematical population models showing that the establishment of MRscan support high levels of biomass (Bensenane et al. 2013) and thatfor sedentary species with dispersal in the larval phase, the bestoutcomes in terms of conservation benefits should be met by re-serves that are large relative to the dispersal distance (Hastings andBotsford 2003; Gerber et al. 2003; Kaplan et al. 2006). Our modelsuggests that reserves of medium size could efficiently protect aba-lone populations inside their boundaries while also ensuring exportof larvae to subsidize recruitment in fished areas and hence would bepreferable to larger reserves if the objective is to maximize abun-dance on the whole coastline.

In addition, our modeling exercise indicates MR networks couldbe established without dramatic losses in fishery performance, pro-vided that the size of individual reserves is adjusted to the species’dispersal ability. In particular, our analysis suggests that the bestoutcomes for H. fulgens, in terms of fishery output, would be achievedwith small reserves �100 m wide. Under these management scenar-ios, reproductive individuals protected inside the reserves can sub-stantially contribute to recruitment in the fishable areas, therebysupporting yields comparable to MSY without MRs. With small re-serves covering less than 40% of the fishing grounds, optimal catchesare only 2%–8% lower than MSY under traditional management (i.e.,in the absence of the reserves). These results confirm and extend toprevious findings for abalone obtained with simplified but analyti-cally tractable mathematical models, suggesting that fishery benefits

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Fig. 5. Long-term abalone yield for the whole island (tonnes fresh mass per year, mean ± SD of the 1000 replicates under the assumption of year-to-year variability in larval dispersaldistance) as a function of protection level (a–c) and harvest rate (d–f) for small reserves of 100 m width (black symbols), intermediate reserves of 500 m width (gray symbols), or withnetworks of large reserves of 1500 m width (white symbols). Dotted line indicates the maximum sustainable yield under traditional management.

0 10 20 30 40 50

05

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30

Protection level (%)

Long

−te

rm y

ield

(t/y

ear)

h=0.1a

0 10 20 30 40 50

05

1015

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30Protection level (%)

Long

−te

rm y

ield

(t/y

ear)

h=0.3b

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rm y

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(t/y

ear)

h=0.7c

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(t/y

ear)

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ear)

PL=10%e

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yie

ld (

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PL=40%f

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are best met by small reserves that maximize larval export outside ofreserves (Hastings and Botsford 2003; Neubert 2003). In the case oflarge reserves (1500 m), in contrast, yields tended to be much smallerthan MSY under traditional management, as individuals in the mid-dle of the reserves cannot contribute to recruitment outside thereserves given the abalone’s limited larval dispersal, here assumed tobe of the scale of hundreds of metres. This is consistent with theresults of previous models on the effect of reserves on abalone yields,which suggested that MRs wider than the species’ larval dispersal

ability would produce catches significantly lower than MSY (Whiteet al. 2010, 2011).

Regarding the effect of reserves on long-term yield, our modelsuggests that the strongest benefit of incorporating networks ofMRs in a fishery management strategy consists in increased ro-bustness to management errors, such as overestimates of sustain-able fishing pressure. Our analyses show that the productioncurve (i.e., the relationship between harvest rate h and yield) isflatter around its peak with MRs than in the case of traditional

Fig. 6. Maximum catches achievable with networks of marine reserves (MRs), expressed as a percentage of traditional maximum sustainableyield (MSY) (i.e., in absence of reserves). Shading indicates size of individual reserves (black symbols: 100 m; gray symbols: 500 m width; whitesymbols: 1500 m width). The dimension of the circle is proportional to the harvest rate required in the fishable patches to maximize catches.

10 20 30 40 50

020

4060

8010

0

Protection Level (%)

Max

imum

cat

ch (

% o

f MS

Y)

h

0.1

0.2

0.3

0.5

Fig. 7. Standardized regression coefficients estimated from the sensitivity analysis of long-term abundances (a) and yields (b) to demographicparameters �E, e, , and � for the scenario with no marine reserves and for the different level of harvest rates.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Harvest rate

Sta

ndar

dize

d R

egre

ssio

n C

oeffi

cien

t

−0.

8−

0.6

−0.

4−

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0.0

0.2

a

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Harvest rate

−0.

8−

0.6

−0.

4−

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0.0

0.2

b

σE e θ α

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management (Fig. 5). Without MRs or with low PLs, the range ofvalues of fishing mortality that provide yields comparable to MSYis narrow (i.e., h = 0.1–0.2), and the yield sharply drops outside thisrange. On the contrary, this range is remarkably larger (up to h =0.8) when more than a third of the fishing ground is protectedinside reserves. This outcome is consistent with the results ofother fishery models, highlighting the ability of MRs to preventcatch decline also when harvest rates are high (Quinn et al. 1993;Sladek-Nowlis and Roberts 1999). This result is important becauseit indicates that exerting excessive harvesting pressure is lesslikely to have deleterious effects on fishery performance and pop-ulation persistence when MRs are part of the management strat-egy. The constant protection of a portion of the stock granted byMRs could in fact prevent the total extirpation of the populationin case of overharvesting. The multiple abalone stock collapsesthat have occurred worldwide suggest that recruitment over-fishing is frequent in the management of this marine mollusk(Sluczanowski 1984; Shepherd et al. 1998a; Leaf et al. 2008). A riskadverse strategy, such as that provided by MR networks, couldthus be desirable for managing remaining abalone stocks and toguard against increasing fishing effort.

The elasticity analysis of the abalone matrix shows that individ-uals in the largest size class have the largest impact on populationgrowth, a result consistent with elasticity analyses conducted onother Haliotis species (Rogers-Bennett and Leaf 2006). Results ofthe sensitivity analysis over the observed range of variation ofmodel parameters confirm that mortality parameters have thegreatest influence on long-term population and catches. Takentogether, these results suggest that (i) conservation efforts shouldbe focused on limiting mortality of large, fecund individuals tomaximize population recovery and (ii) events of increased mortal-ity, such as those recently observed on the island due to adverseenvironmental conditions (hypoxia) (Micheli et al. 2012), couldhave a strong deleterious effect on stocks and on related harvests.

Our results confirm previous findings that for sedentary specieswith limited larval dispersal, the goal of maintaining catches is bestachieved by many small reserves covering a large fraction of thecoast, alternated with fished areas (Hastings and Botsford 2003;Neubert 2003). In Isla Natividad, the fishing cooperative has decidedto maintain the existing reserves and is currently in the process ofdeciding whether to expand protection through additional reserves.Additional communities to the north and south of Isla Natividadhave also established MRs. According to our results, the size of thetwo existing reserves in Isla Natividad (�500 and 1000 m) seemsadequate to protect the abalone stock inside their boundaries, butshould be reduced to maximize fishery benefits. In addition, theoverall level of protection (�8%) is probably too small; the number ofreserves should be increased to successfully ensure population per-sistence and to increase long-term yield. Clearly, our results arebased on the underlying assumption that depleted populations ofH. fulgens could recover if exploitation is reduced; however, addi-tional stressors such as climate change and diseases can also nega-tively affect abalone persistence (e.g., Miner et al. 2006), and therecovery of abalone populations inside MRs cannot be guaranteed.

Results of the present model are clearly sensitive to assump-tions about the larval dispersal ability of abalone that we based onboth existing literature (see above) and our recruitment studies(Micheli et al. 2012). Dispersal distance is a critical variable that isdifficult to measure in the natural environment and is thereforeaffected by great uncertainty. Additional studies on the larvaldispersal ability of marine organisms can help ameliorate theconfidence in the quantitative results of population dynamicsimulations. In addition, in our modeling study, we assumed com-plete homogeneity in habitat and symmetry in dispersal. In real-ity, however, marine habitats are heterogeneous; some areas mayfunction as larval sources and other as sinks. In addition, currentsand other coastal oceanographic features may drive the dispersalin a given direction and create barriers to dispersal in other direc-

tions. Understanding if there are major spatial patterns in habitatproductivity and in dominant oceanographic currents could fur-ther guide the improvement of an MRs network.

Along the Baja California and California coasts, the implemen-tation of networks of small MRs is expected to be beneficial notonly for abalones, but also for other marine invertebrates withsimilar life history characteristics (long-lived sedentary adults anddispersing larval stages), such as sea urchins, turban snails, andsea cucumbers, that are currently important fisheries in Mexico(McCay et al. 2014) and are expected to become increasingly im-portant fisheries in California (Rogers-Bennett et al. 2007). Whilesuch a network has been established in California through theMarine Life Protection Act, it does not exist in Baja California.Extending the existing US network to the south, along the coast ofBaja California, through the establishment of opportunely spacedMRs, is expected to improve the population status, yields, andsustainability of the benthic invertebrate fisheries in the area.

AcknowledgementsMarisa Rossetto was supported through the EU grant “Towards

COast to COast NETworks of marine protected areas”, FiorenzaMicheli by the Walton Family Foundation and the US NSF-CNHprogram (award No. DEB-1212124), and Giulio De Leo by the USNSF-OA program (agreement No. OCE-1416934). We thank mem-bers and staff of the fishing cooperative Buzos y Pescadores fortheir support and advice, Marino Gatto for his friendly review,and three anonymous referees for their constructive criticism onearly versions of the manuscript.

ReferencesAviles, J.G.G., and Shepherd, S.A. 1996. Growth and survival of the blue abalone

Haliotis fulgens in barrels at Cedros Island, Baja California, with a review ofabalone barrel culture. Aquaculture, 140: 169–176. doi:10.1016/0044-8486(95)01199-4.

Bardos, D.C. 2005. Probabilistic Gompertz model of irreversible growth. Bull.Math. Biol. 67: 529–545. doi:10.1016/j.bulm.2004.08.009.

Bensenane, M., Moussaoui, A., and Auger, P. 2013. On the optimal size of marinereserves. Acta Biotheor. 61: 109–118. doi:10.1007/s10441-013-9173-9. PMID:23381499.

Botsford, L.W., Hastings, A., and Gaines, S.D. 2001. Dependence of sustainabilityon the configuration of marine reserves and larval dispersal distance. Ecol.Lett. 4: 144–150. doi:10.1046/j.1461-0248.2001.00208.x.

Botsford, L.W., Micheli, F., and Hastings, A. 2003. Principles for the design ofmarine reserves. Ecol. Appl. 13: 25–31. doi:10.1890/1051-0761(2003)013[0025:PFTDOM]2.0.CO;2.

Button, C.A., and Rogers-Bennett, L. 2011. Vital rates of pink abalone Haliotiscorrugata estimated from mark–recapture data to inform recovery. Mar. Ecol.Progr. Ser. 431: 151–161. doi:10.3354/meps09094.

Caswell, H. 2001. Matrix population models: construction, analysis, and inter-pretation. 2nd ed. Sinauer Associates, Sunderland, Mass.

Caswell, H., Takada, T., and Hunter, C.M. 2004. Sensitivity analysis of equilib-rium in density-dependent matrix population models. Ecol. Lett. 7: 380–387.doi:10.1111/j.1461-0248.2004.00595.x.

Connell, J.H. 1985. The consequences of variation in initial-settlement vs. post-settlement mortality in rocky intertidal communities. J. Exp. Mar. Biol. Ecol.93: 11–45. doi:10.1016/0022-0981(85)90146-7.

Cross, P.C., and Beissinger, S.R. 2001. Using logistic regression to analyze thesensitivity of PVA models: a comparison of methods based on African wilddog models. Conserv. Biol. 15: 1335–1346. doi:10.1046/j.1523-1739.2001.00031.x.

Daume, S., Huchette, S., Ryan, S., and Day, R.W. 2004. Nursery culture of Haliotisrubra: the effect of cultured algae and larval density on settlement and juve-nile production. Aquaculture, 236: 221–239. doi:10.1016/j.aquaculture.2003.09.035.

Day, R., Gilmour, P., and Huchette, S. 2004. Effects of density and food supply onpostlarval abalone: behaviour, growth and mortality. J. Shellfish Res. 23:1009–1018.

Dichmont, C.M., Butterworth, D.S., and Cochrane, K.L. 2000. Towards adaptiveapproaches to management of the South African abalone Haliotis midaefishery. South Afr. J. Mar. Sci. 22: 33–42. doi:10.2989/025776100784125753.

Durazo-Beltrán, E., Toro-Vázquez, J.F., Vásquez-Peláez, C., and Viana, M.T. 2003.Effect of the seaweed Macrocystis pyrifera and a formulated diet on growth andfatty acid composition in the green abalone, Haliotis fulgens, under commer-cial culture conditions. Cienc. Mar. 29: 645–654.

Edgar, G.J., and Barrett, N.S. 1999. Effects of the declaration of marine reserveson Tasmanian reef fishes, invertebrates and plants. J. Exp. Mar. Biol. Ecol.242: 107–144. doi:10.1016/S0022-0981(99)00098-2.

Pagination not final (cite DOI) / Pagination provisoire (citer le DOI)

Rossetto et al. 13

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. J. F

ish.

Aqu

at. S

ci. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y ST

AN

FOR

D U

NIV

. on

08/2

4/15

For

pers

onal

use

onl

y.

Gaines, S.D., White, C., Carr, M.H., and Palumbi, S.R. 2010. Designing marinereserve networks for both conservation and fisheries management. Proc.Natl. Acad. Sci. U.S.A. 107: 18286–18293. doi:10.1073/pnas.0906473107. PMID:20200311.

Gell, F.R., and Roberts, C.M. 2003. Benefits beyond boundaries: the fishery effects ofmarine reserves. TREE, 18: 448–455. doi:10.1016/S0169-5347(03)00189-7.

Gerber, L.R., Botsford, L.W., Hastings, A., Possingham, H.P., Gaines, S.D.,Palumbi, S.R., and Andelman, S. 2003. Population models for marine reservedesign: a retrospective and prospective synthesis. Ecol. Appl. 13: S47–S64.doi:10.1890/1051-0761(2003)013[0047:PMFMRD]2.0.CO;2.

Guzmán del Próo, S.A., and Lopez-Salas, F. 1993. Crecimiento de Haliotis fulgens en BahíaAsunción. Baja California Sur, Mexico. An. Esc. Nac. Cienc. Biol. 38: 59–66.

Guzmán del Próo, S.A., Salinas, F., Zaytsev, O., Belmar-Pérez, J., andCarillo-Laguna, J. 2000. Potential dispersion of reproductive products andlarval stages of abalone (Haliotis spp.) as a function of the hydrodynamics ofBahía Tortugas, Mexico. J. Shellfish Res. 19: 869–881.

Halpern, B.S., and Warner, R.R. 2003. Matching marine reserve design to reserveobjectives. Proc. R. Soc. B Biol. Sci. 270: 1871–1878. doi:10.1098/rspb.2003.2405.

Hastings, A., and Botsford, L.W. 1999. Equivalence in yield from marine reservesand traditional fisheries management. Science, 284: 1537–1538. doi:10.1126/science.284.5419.1537. PMID:10348743.

Hastings, A., and Botsford, L.W. 2003. Comparing designs of marine reserves forfisheries and for biodiversity. Ecol. Appl. 13(Suppl.): 65–70. doi:10.1890/1051-0761(2003)013[0065:CDOMRF]2.0.CO;2.

Holland, D.S., and Brazee, R.J. 1996. Marine reserves for fisheries management.Mar. Res. Econ. 11: 157–172.

Kaplan, D.M., Botsford, L.W., and Jorgensen, S. 2006. Dispersal per recruit: anefficient method for assessing sustainability in marine reserve networks.Ecol. Appl. 16: 2248–2263. doi:10.1890/1051-0761(2006)016[2248:DPRAEM]2.0.CO;2. PMID:17205902.

Karpov, K.A., Haaker, P.L., Taniguchi, I.K., and Rogers-Bennett, L. 2000. Serialdepletion and the collapse of the California abalone (Haliotis spp.) fishery. InWorkshop on Rebuilding Abalone Stocks in British Columbia. Edited byA. Campbell. Can. Spec. Publ. Fish. Aquat. Sci. No. 130. pp. 11–24.

Lauck, T., Clarke, C.W., Mangel, M., and Munro, G.R. 1998. Implementing theprecautionary principles in fisheries management through marine reserves.Ecol. Appl. 8: S72–S78. doi:10.1890/1051-0761(1998)8[S72:ITPPIF]2.0.CO;2.

Leaf, R.T., Rogers-Bennett, L., and Jiao, Y. 2008. Exploring the use of a size-basedegg-per-recruit model for the red abalone fishery in California. N. Am. J. Fish.Manage. 28:1638–1647. doi:10.1577/M07-132.1.

Leslie, H., Ruckelshaus, M., Ball, I.R., Andelman, S., and Possingham, H.P. 2003.Using siting algorithms in the design of marine reserve networks. Ecol. Appl.13: S185–S198. doi:10.1890/1051-0761(2003)013[0185:USAITD]2.0.CO;2.

Lester, S.E., Halpern, B.S., Grorud-Colvert, K., Lubchenco, J., Ruttenberg, B.I.,Gaines, S.D., Airamé, S., and Warner, R.R. 2009. Biological effects withinno-take marine reserves: a global synthesis. Mar. Ecol. Prog. Ser. 384: 33–46.doi:10.3354/meps08029.

Maliao, R.L., Webb, E.L., and Jensen, K.R. 2004. A survey of stock of the donkey’sear abalone, Haliotis asinina L. in the Sagay Marine Reserve, Philippines: eval-uating the effectiveness of marine protected area enforcement. Fish. Res. 66:343–353. doi:10.1016/S0165-7836(03)00181-4.

Mangel, M. 2000. Irreducible uncertainties, sustainable fisheries and marinereserves. Evol. Ecol. Res. 2: 547–555.

McCarthy, M.A., Burgman, M.A., and Ferson, S. 1995. Sensitivity analysis formodels of population viability. Biol. Conserv. 73: 93–100. doi:10.1016/0006-3207(95)90029-2.

McCay, B.J. , Micheli, F., Ponce-Díaz, G., Murray, G., Shester, G.,Ramirez-Sanchez, S., and Weisman, W. 2014. Cooperatives, concessions, andco-management on the Pacific coast of Mexico. Mar. Pol. 44: 49–59. doi:10.1016/j.marpol.2013.08.001.

McCormick, T.B., Aguirre, A., Mill, T.S., and Herbinson, K.T. 1992. Growth andsurvival of red (Haliotis rufescens), green (H. fulgens), and pink (H. corrugata)abalone in land- and ocean-based cultivation systems. Fish. Res. Pap. Dep.Fish. (S. Aust.), 24: 49–60.

McShane, P.E. 1991. Density-dependent mortality of recruits of the abalone Haliotis rubra(Mollusca: Gastropoda). Mar. Biol. 110: 385–389. doi:10.1007/BF01344357.

McShane, P.E. 1992. Early life of abalone: a review. In Abalone of the world:biology, fisheries and culture. Edited by S.A. Shepherd, M.J. Tegner, and S.A.Guzman del Proo. pp. 120–140.

McShane, P.E., Black, K.P., and Smith, M.G. 1988. Recruitment processes inHaliotis rubra (Mollusca: Gastropoda) and regional hydrodynamics in south-eastern Australia imply localized dispersal of larvae. J. Exp. Mar. Biol. Ecol.124: 175–203. doi:10.1016/0022-0981(88)90171-2.

Micheli, F., Halpern, B.S., Botsford, L.W., and Warner, R.R. 2004. Trajectories andcorrelates of community change in no-take marine reserves. Ecol. Appl. 14:1709–1723. doi:10.1890/03-5260.

Micheli, F., Shelton, A.O., Bushinsky, S.M., Chiu, A.L., Haupt, A.J., Heiman, K.W.,Kappel, C.V., Lynch, M.C., Martone, R.G., Dunbar, R.B., and Watanabe, J. 2008.Persistence of depleted abalones in marine reserves of central California.Biol. Conserv. 141: 1078–1090. doi:10.1016/j.biocon.2008.01.014.

Micheli, F., Saenz-Arroyo, A., Greenley, A., Vazquez, L., Espinoza, Montes, J.A.,Rossetto, M., and De Leo, G.A. 2012. Evidence that marine reserves enhance

resilience to climatic impacts. PLoS ONE, 7: e40832. doi:10.1371/journal.pone.0040832. PMID:22855690.

Miner, C.M., Altsatt, J.M., Raimondi, P.T., and Minchinton, T.E. 2006. Recruit-ment failure and shifts in community structure following mass mortalitylimit recovery prospects of black abalone. Mar. Ecol. Prog. Ser. 327: 107–117.doi:10.3354/meps327107.

Morales-Bojórquez, E., Muciño-Díaz, M.O., and Vélez-Barajas, J.A. 2008. Analysisof the decline of the abalone Fishery (Haliotis fulgens and H. corrugata) alongthe Westcentral Coast of the Baja California Peninsula, Mexico. J. ShellfishRes. 27:865–870. doi:10.2983/0730-8000(2008)27[865:AOTDOT]2.0.CO;2.

Neubert, M.G. 2003. Marine reserves and optimal harvesting. Ecol. Lett. 6: 843–849. doi:10.1046/j.1461-0248.2003.00493.x.

Parnell, P.E., Lennert-Cody, C.E., Geelen, L., Stanley, L.D., and Dayton, P.K. 2005.Effectiveness of a small marine reserve in southern California. Mar. Ecol.Progr. Ser. 296: 39–52. doi:10.3354/meps296039.

Ponce-Díaz, G., Vega-Velázquez, A., Ramade-Villanueva, M., León-Carballo, G.,and Franco-Santiago, R. 1998. Socioeconomic characteristics of the abalonefishery along the west coast of the Baja California peninsula, México. J. Shell-fish Res. 17: 853–857.

Prince, J.D., Sellers, T.L., Ford, W.B., and Talbot, S.R. 1988. Confirmation of arelationship between the localized abundance of breeding stock and recruit-ment for Haliotis rubra Leach (Mollusca: Gastropoda). J. Exp. Mar. Biol. Ecol.122: 91–104. doi:10.1016/0022-0981(88)90178-5.

Quinn, J.F., Wing, S.R., and Botsford, L.W. 1993. Harvest refugia in marineinvertebrate fisheries: models and applications to the red sea urchin,Strongylocentrotus franciscanus. Am. Zool. 33: 537–550. doi:10.1093/icb/33.6.537.

Roberts, C.M., Bohnsack, J.A., Gell, F., Hawkins, J.P., and Goodridge, R. 2001.Effects of marine reserves on adjacent fisheries. Science, 294: 1920–1923.doi:10.1126/science.294.5548.1920. PMID:11729316.

Rodríguez-Valencia, J.A., Caballero-Alegría, F., and Castro-González, J. 2004.Temporal trends (1989–1999) in populations of Haliotis fulgens and H. corrugata(Gastropoda: Haliotidae) from Cedros Island, Baja California, Mexico. Cienc.Mar. 30: 489–501.

Rogers-Bennett, L., and Leaf, R.T. 2006. Elasticity analyses of size-based red andwhite abalone matrix models: management and conservation. Ecol. Appl. 16:213–224. doi:10.1890/04-1688. PMID:16705974.

Rogers-Bennett, L., Haaker, P.A., Huff, T.O., and Dayton, P.K. 2002. Estimatingbaseline abundances of abalone in California for restoration. Calif. Coop.Ocean. Fish. Investig. Rep. 43: 97–111.

Rogers-Bennett, L., Rogers, D.W., and Schultz, S.A. 2007. Modeling growth andmortality of red abalone (Haliotis rufescens) in northern California. J. ShellfishRes. 26(3): 719–727. doi:10.2983/0730-8000(2007)26[719:MGAMOR]2.0.CO;2.

Rossetto, M., De Leo, G.A., Bevacqua, D., and Micheli, F. 2012. Allometric scalingof mortality rates with body mass in abalones. Oecologia, 168: 989–996.doi:10.1007/s00442-011-2163-1. PMID:22020817.

Rossetto, M., De Leo, G.A., Greenley, A., Vazquez, L., Saenz-Arroyo, A.,Espinoza-Montes, J.A., and Micheli, F. 2013. Reproductive potential can pre-dict recruitment rates in abalone. J. Shellfish Res. 32: 161–169. doi:10.2983/035.032.0122.

Sasaki, R., and Shepherd, S.A. 1995. Larval dispersal and recruitment of Haliotisdiscus hannai and Tegula spp. on Miyagi Coasts, Japan. Mar. Freshw. Res. 46:519–529. doi:10.1071/MF9950519.

Shanks, A.L., Grantham, B.A., and Carr, M.H. 2003. Propagule dispersal distanceand the size and spacing of marine reserves. Ecol. Appl. 13: 159–169. doi:10.1890/1051-0761(2003)013[0159:PDDATS]2.0.CO;2.

Shepherd, S.A. 1990. Studies on southern Australian abalone (genus Haliotis).XII. Long-term recruitment and mortality dynamics of an unfished popula-tion. Aust. J. Mar. Freshw. Res. 41: 475–492. doi:10.1071/MF9900475.

Shepherd, S.A., Guzmán del Próo, S.A., Turrubiates, J., Belmar, J., Baker, J.L., andSluczanowski, P.R. 1991. Growth, size at sexual maturity and Egg-per-recruitanalysis of the abalone Haliotis fulgens in Baja California. Veliger, 34: 324–330.

Shepherd, S.A., Lowe, D., and Partington, D. 1992. Studies on southern Austra-lian abalone (genus Haliotis). XIII. larval dispersal and recruitment. J. Exp.Mar. Biol. Ecol. 164: 247–260. doi:10.1016/0022-0981(92)90178-D.

Shepherd, S.A., Turrubiates-Morales, J.R., and Hall, K. 1998a. Decline of the Ab-alone fishery at la Natividad, Mexico: overfishing or climate change? J. Shell-fish Res. 17: 839–846.

Shepherd, S.A., Lowe, D., and Partington, D. 1998b. Studies on Southern Austra-lian abalone (genus Haliotis). XIX: long-term juvenile mortality dynamics.J. Shellfish Res. 17: 813–825.

Sladek-Nowlis, J., and Roberts, C.M. 1999. Fisheries benefits and optimal designof marine reserves. Fish. Bull. 97: 604–616.

Sluczanowski, P.R. 1984. A management oriented model of an abalone fisherywhose substocks are subject to pulse fishing. Can. J. Fish. Aquat. Sci. 41(7):1008–1014. doi:10.1139/f84-117.

Tegner, M.J., and Butler, R.A. 1985. Drift-tube study of the dispersal potential ofgreen abalone (Haliotis fulgens) in the southern California bight: implicationsfor recovery of depleted populations. Mar. Ecol. Progr. Ser. 26: 73–84. doi:10.3354/meps026073.

Temby, N., Miller, K., and Mundy, C. 2007. Evidence of genetic subdivisionamong populations of blacklip abalone (Haliotis rubra Leach) in Tasmania.Mar. Freshw. Res. 58: 733–742. doi:10.1071/MF07015.

Pagination not final (cite DOI) / Pagination provisoire (citer le DOI)

14 Can. J. Fish. Aquat. Sci. Vol. 72, 2015

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. J. F

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pres

s.co

m b

y ST

AN

FOR

D U

NIV

. on

08/2

4/15

For

pers

onal

use

onl

y.

Tutschulte, T.C. 1976. The comparative ecology of three sympatric abalones.Ph.D. thesis, University of California, San Diego, Calif.

Wallace, S.S. 1999. Evaluating the effects of three forms of marine reserve onNorthern abalone populations in British Columbia, Canada. Conserv. Biol.13: 882–887. doi:10.1046/j.1523-1739.1999.98117.x.

White, J.W., Botsford, L.W., Moffitt, E.A., and Fischer, D.T. 2010. Decision analysis fordesigning marine protected areas for multiple species with uncertain fisherystatus. Ecol. Appl. 20: 1523–1541. doi:10.1890/09-0962.1. PMID:20945757.

White, J.W., Botsford, L.W., Baskett, M.L., Barnett, L.A.K., Barr, R.J., andHastings, A. 2011. Linking models with monitoring data for assessing per-formance of no-take marine reserves. Front. Ecol. Environ. 9: 390–399.doi:10.1890/100138.

Appendix AAccording to Bardos (2005), the probability of a length increment �ly

conditional on initial length ly in the yth tag–recapture record is

(A1) p(�ly�ly) ���

�(�)(L∞ � ly)

��1e��(L∞�ly) 1

1 � e�G��ly � lyly

�1

e�G�1

where

(A2) L∞ � (ly � �ly)ly�e�G�

1

1�e�G

(A3) � �Ln

1 � ��lyLn�3/� �L

1 � � lyLn�3 2

(A4) � � � Ln

1 � ��lyLn�3/ �L

1 � � lyLn�3 2

The five parameters of the Gompertz growth function (G, Ln, �L2,

�, and ) were estimated by minimizing the following negativelog-likelihood function deriving from eq. A1:

(A5) �log(L) � �y

�logp(�ly�ly)�

The growth transition gi,j from initial class j in the interval (r1,r2)to final class i in the interval (r3,r4) was then calculated as a doubleintegral of p(�l | l1) over initial and final lengths across size classes iand j, respectively (Bardos 2005):

(A6) gi,j �1

r2 � r1�r1

r2

dly �r3�ly

r4�ly

p(�ly�ly)d�ly

The resulting matrix of growth transitions gi,j is shown inTable A1.

Table A1. Growth transition gi,j from initial class j to final class i.

Size class j (mm)

Size class i (mm) 5–30 30–55 55–80 80–105 105–130 130–155 155–180 180–205 205–230

5–30 0.166 0 0 0 0 0 0 0 030–55 0.590 0.02 0 0 0 0 0 0 055–80 0.242 0.533 0.014 0 0 0 0 0 080–105 0.003 0.429 0.553 0.028 0 0 0 0 0105–130 0 0.018 0.424 0.77 0.102 0 0 0 0130–155 0 0 0.008 0.202 0.878 0.317 0 0 0155–180 0 0 0 0 0.02 0.683 0.549 0 0180–205 0 0 0 0 0 0 0.451 0.694 0205–230 0 0 0 0 0 0 0 0.306 1

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