Spatial Management for Protogynous Sex-Changing Fishes: a General Framework for Coastal Systems

Vol. 543: 223–240, 2016 MARINE ECOLOGY PROGRESS SERIES Published February 3 doi: 10.3354/meps11574 Mar Ecol Prog Ser

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Spatial management for protogynous sex-changing fishes: a general framework for coastal systems

Erin E. Easter*, J. Wilson White

Department of Biology and Marine Biology, University of North Carolina Wilmington, 601 S. College Road, Wilmington, NC 28403, USA

ABSTRACT: Most models of fish population dynamics ignore differences between male and female fish. Yet many harvested species are protogynous hermaphrodites (older females change sex into males), so size-selective fishing will disproportionately remove males. This shifts the sex ratio, potentially disrupting reproduction. Some modeling studies have investigated management strategies for protogynous fishes, but there is no general theory explaining how spatial fishery management should account for protogyny. We developed a spatially explicit model of a generic protogynous fish population to examine the factors affecting the population persistence of coastal (i.e. non-migratory) protogynous populations under spatial management. We varied both (1) biological factors— the cues triggering sex change and the mating function (the relationship between sex ratio and fertilization success) and (2) management factors — configuration of no-take reserves and fishery management outside reserve boundaries. We found that the number and size of reserves required for persistence depended strongly on the sex change cue and the shape of the mating function. Populations with less flexible sex change and requiring more males for fertilization needed more and larger reserves. Unfortunately, empirical mating functions are poorly known for most species and a worthy target of future research. Additionally, persistence of populations with less flexible sex change was impaired by fishery regulations that concentrated on male size classes outside of reserves. Finally, we found that increases in the sex ratio (proportion male) inside reserves are not a reliable indicator of reserve success. These results can be used to design spatial management plans and to set expectations for management assessments.

KEY WORDS: Marine reserve · Marine protected area · Sex change · Sequential hermaphrodite · Protogyny · Mating function

INTRODUCTION models that describe the response of populations to marine reserves, usually focusing on population per- Spatial management strategies, including the use sistence and fishery yield (reviewed by White et al. of marine protected areas (MPAs), are increasingly 2011). Most such models assume sexes are fixed and used to address biodiversity conservation and fishery in equal proportions and ignore the effects of harvest management goals (Wood et al. 2008). While many on sex-specific survival, reproductive patterns, and MPAs are partial-take, both empirical and model fertilization success (but see Heppell et al. 2006, analyses have focused on no-take marine reserves in Alonzo et al. 2008, Chan et al. 2012). The oversimpli- developing spatial management strategies for sup- fication that females solely contribute to reproductive porting sustainable fisheries (e.g. Halpern et al. 2009, success persists largely because females produce Gaines et al. 2010). Reserve design principles are eggs (assumed to be the limiting gamete), and in often based on the predictions of spatially explicit many species, males can mate and spawn with multi-

© The authors 2016. Open Access under Creative Commons by *Corresponding author: [email protected] Attribution Licence. Use, distribution and reproduction are un - restricted. Authors and original publication must be credited. Publisher: Inter-Research · www.int-res.com 224 Mar Ecol Prog Ser 543: 223–240, 2016

ple females (Heppell et al. 2006). These assumptions are grouped into endogenous cues (a fixed develop- may be appropriate for gonochoristic (separate-sex) mental schedule, such as size, condition, or age) or species, because males and females are typically of exogenous cues (flexible social or environmental similar body size, so size-selective fishing targets cues; Armsworth 2001). Most models of protogynous both sexes equally and does not affect the population fish population dynamics have shown that if sex sex ratio. However, this is not true for the many fish change is determined by a fixed developmental species that are sequential hermaphrodites, i.e. that schedule, size-selective fishing effort may be more change sex during their lifetime. de trimental to the sex ratio than in an exogenously The most common type of sequential hermaphro- cued population, in which removal of males will trig- ditism in exploited species is protogyny (species ger sex change, compensating for the shift in sex which reproduce as females first and then change ratio (Alonzo & Mangel 2005, Ellis & Powers 2012). sex to male). Many commercially and recreationally While exogenously cued sex change may prevent de - important species exhibit protogyny, including Cali- leterious shifts in the sex ratio and consequent sperm fornia sheephead Semicossyphus pulcher, black sea limitation, protogynous populations often experience bass Centropristis striata, gag grouper Mycteroperca sexual maturity and transformation at smaller sizes or microlepis, red grouper Ephinephelus morio, red younger ages and slower growth rates when fisheries porgy Pagrus pagrus, and coral trout Plectropomus are size selective for the largest individuals, which leopardus, along with a number of aquarium trade likely reduce the average body size and sex-specific species (e.g. bicolor parrotfish Cetoscarus bicolor, fecundity (Hamilton et al. 2007). Discrepancies exist bluehead wrasse Thalassoma bifasciatum, rainbow in the literature regarding the effect of fishing effort wrasse T. lucasanum) and live-fish fishery species and marine reserve implementation on the various (humphead wrasse Cheilinus undulatus, brown- sex change patterns; however, a consensus suggests marbled grouper E. fuscoguttatus) (reviewed by De that simply knowing that a population exhibits pro- Mitcheson & Liu 2008). togyny is not enough to develop successful manage- The complex life history of protogynous hermaph- ment strategies (Alonzo & Mangel 2005, Ellis & Pow- rodites creates a challenge for spatial management, ers 2012; but see Grüss et al. 2014). as mathematical models have historically focused on Existing research on spatial management strategies gonochore fish populations. Size-selective fisheries for protogynous hermaphrodites has largely focused are of particular concern for protogynous species, as on tactical or system-specific situations, such as re- the take of the largest (and thus predominantly male) serve designs for a particular species or population individuals may skew sex ratios and lead to sperm (e.g. Huntsman & Schaaf 1994, Heppell et al. 2006, limitation (Coleman et al. 1996, McGovern et al. Little et al. 2007, Mapstone et al. 2008, Chan et al. 1998, Hawkins & Roberts 2004, Hamilton et al. 2007), 2012, Ellis & Powers 2012), which limits the applica- reducing the reproductive output of the population. bility of model results and the general theory derived Fishing mortality, even when distributed evenly by those studies. For example, Heppell et al. (2006) among age classes, may skew sex ratios towards and Ellis & Powers (2012) both modeled gag grouper females in protogynous populations by reducing the M. microlepis populations under different manage- number of individuals reaching the age or size class ment scenarios in the northern Gulf of Mexico, threshold for changing sex (Heppell et al. 2006). finding that enacting spawning site reserves re sulted Extreme shifts in the sex ratio are assumed to lead to in the greatest sex ratio improvements by reducing sperm limitation and thus reduce the reproductive fishing mortality on both adult males and females. output of the population (Alonzo et al. 2008), al - Their analysis focused largely on the details of the though the empirical relationship between sex ratio study species’ life history (i.e. annual spawning mi- and fertilization success (the mating function, sensu grations and the role of an inshore fishery for Miller & Inouye 2011) is largely unknown. Under females). Modeling the common coral trout P. leopar- spatial management, the sex ratio will differ between dus on the Great Barrier Reef (Australia), Chan et al. fished and unfished areas, creating heterogeneity in (2012) investigated the differences between a gono- reproductive output that is not accounted for in spa- chore and protogynous population, considering a sin- tial models of gonochores (Chan et al. 2012). gle sex change rule, specifically with the goal of un- The response of protogynous fish populations to derstanding how marine reserves will affect fishery spatial management likely also depends on the cues yields in each population. Chan et al. (2012) found that trigger sex change (Alonzo & Mangel 2005). that sex-changing populations in no-take reserve Generally, the signals that initiate sexual transition scenarios did not receive the yield-increasing benefits Easter & White: Spatial management for coastal protogynous sex-changing fishes 225

of marine reserves compared to non-sex-changing fishing regulations outside reserves. From these sim- populations because males are likely to be dispropor- ulations, we updated 2 key guidelines for spatial tionately distributed between reserves (high propor- management (minimum reserve size and total re - tion of males) and unprotected areas (low proportion serve area) to ensure persistence of protogynous of males). They concluded that the disproportionate hermaphrodite populations. In our analysis, we distribution reduced the average contribution of focused on coastal or reef-dwelling protogynous males to fertilization success and thus lowered pro- fishes for which size and spacing guidelines would ductivity. That result arose because the mating func- be applicable. Protogynous fishes with ontogenetic tion they used had negative concavity, so the average or spawning migrations will require distinct spatial fertilization over space was lower than one would ex- management approaches (e.g. Heppell et al. 2006, pect from the average sex ratio over space (an in- White 2015) that we do not address here. Our analy- stance of Jensen’s inequality; Ruel & Ayres 1999). sis explored the generality of our prescriptions for However, while noting the potential importance of spatial management and the need for better empiri- males to reserve performance, Chan et al. (2012) did cal characterization of uncertain biological factors. not fully explore the sensitivity of their results to the shape of the mating function in their model. In contrast to the complex and situation- or species- METHODS specific nature of such tactical models, which are often used to make local management decisions We used a discrete-time, spatially explicit, age- (Gerber et al. 2003, White et al. 2010a, 2013), strate- structured model of a generic protogynous hermaph- gic models are generally simpler and address broad rodite population (adapted from White & Rogers-Ben- questions, such as what fraction of the coastline nett [2010] and Alonzo & Mangel [2005]) to predict should be placed within reserves, to generate gen- adult sex ratio, fertilization rate, and biomass as a eral spatial management rules of thumb which are function of size-specific fishing mortality. We focused more widely applicable (Botsford et al. 2003, Gerber on equilibrium dynamics (static population size and et al. 2003, White et al. 2010b, Moffitt et al. 2011). sex distribution), so simulations were started with ar- Strategic models can also provide guiding principles bitrary initial conditions and run for 1000 time steps which aid in interpreting the results of tactical mod- (sufficient to reach equilibrium, for simulations with els (Gerber et al. 2003, White et al. 2011). Most exist- persistent populations); we then analyzed results at ing theoretical models for the spatial management of the final time step. The population occupied a 1- protogynous stocks have been tactical in nature, and dimensional, infinite coastline (to eliminate edge arti- as such, general principles derived from strategic facts) with homogeneous habitat, simulated as a cir- models describing the factors that determine when cular array of n spatial cells, each defined as reserve and why protogynous populations should be man- or non-reserve (similar to the models of Botsford et al. aged differently from gonochores are lacking. We 2001, White et al. 2010b). All variables used in the examined how spatial management theory for model are defined in Table 1, and all fixed parameters coastal environments should accommodate species and their values are given in Table 2. Matlab model with protogynous life histories, considering a broader code is available at https:// github.com/jwilsonwhite/ range of life histories, maturation and sex change protogynous_spatial_ model. rules, and mating function parameters than previ- The basic structure of the model is as follows: in ously noted studies to draw more broadly applicable each time step, the subpopulation within each spatial conclusions. We compared models of generic protog- cell ages 1 yr and experiences somatic growth and ynous hermaphrodite populations with various sex both natural mortality and age-specific fishing mor- change cues (both fixed and flexible) to a model of an tality. The population spawns larvae, with reproduc- otherwise identical gonochore population in various tive output dependent on the sex ratio within the spatial management and fishery scenarios. We inves- patch and the mating function. The larvae disperse to tigated the sensitivity of our results to 2 key sources other cells in the landscape and experience intra- of biological uncertainty, the sex change cue (endo - cohort density-dependent mortality at settlement. genous vs. exogenous) and the mating function relat- Finally, the population sex ratio is adjusted based on ing the sex ratio to fertilization success (i.e. how the updated population size distribution and sex important are males to reproduction), and 2 manage- ratio, depending on the particular sex change cue ment factors that may affect reserves, the intensity of being simulated. We now provide details on each fishing outside reserve boundaries and size-based element of the model. 226 Mar Ecol Prog Ser 543: 223–240, 2016

Table 1. Model variables and their definitions here for simplicity we focused on the case with no advection (μ = 0) but varied σ. Symbol Definition With the incorporation of sex change and the contribution of both females and males to reproductive Larval dispersal/recruitment output, the number of settlers arriving at cell i at time dij Probability of dispersal from cell j to cell i t, Si,t, is: Si,t Settler density in cell i at time t n N n × 1 vector of fish abundance in each age class t,j SdPLNf() (1) at time t in cell j it, = ∑ ij t,, j t j i=1 f(L) n × 1 vector of female fecundity as a function of length, L where Nt,j is an n × 1 vector of fish abundance in each age class at time t in patch j; f(L) is an n × 1 vector of Ri,t Number of recruits to age 1 in cell i at time t female fecundity as a function of length, L (see Growth and reproduction below, Eq. 4); and Pt,j is the proportion of eggs fertil- La Length at age a ized at time t in patch j (see below, Eq. 5), which f(L) Vector of eggs produced at each body length La depends on the population sex ratio. The probability

f(La) Eggs produced at body length La of larval dispersal from j to i, dij, is given by the dis- Pt,j Proportion of fertilized eggs at time t in cell j persal kernel described above. Note that bold

Bt,i Proportional male biomass upright symbols indicate matrices, lowercase itali- cized symbols are scalars, uppercase indicates state Adult survival variables, lowercase indicates parameters (either Fi Size-specific fishing mortality in cell i, repre-  sented in terms of FLEP Roman or Greek characters), and is the transpose LEP Lifetime egg production; mean reproductive operator. effort of a new recruit The number of recruits to age 1 at cell i, Ri,t, is com- FLEP Fraction of unfished LEP realized by a fished prised of the number of settlers Si that survive den- population sity-dependent mortality according to a Beverton- CRT Critical replacement threshold; minimum value Holt function: of FLEP required for population persistence αSit, Rit, = s(La) Fishery harvest selectivity α (2) σ 1+ Sit, i(La) Annual adult survival in cell i β where α is density-independent survivorship (de - Maturity and sex change scribing the slope of the settler-recruit curve at low Si,t Frequency of smaller mature individuals in cell i at time t population density), and β is the asymptotic maximum number of settlers S that can survive to recruit p M(La) Probability of maturation at length L i,t in a cell. pc(La) Probability of sex change at length L Larval dispersal was the only mode of movement Marine reserves be tween habitat cells that we considered. Many CR Fraction of coastline within reserve fishes also exhibit adult movement within home WR Width of individual reserve (km) ranges that could extend beyond the boundaries of a single marine reserve, but the general effects of that type of movement on reserve performance are Larval dispersal and recruitment already well characterized (e.g. Moffitt et al. 2009, 2011, 2013). There is no reason to expect that a sex- To represent pelagic larval dispersal, larvae pro- changing life history would alter the generally nega- duced in each spatial cell dispersed to adjacent cells tive effects of adult movement on population persist- according to a Gaussian dispersal kernel in which ence within reserves, so we kept our analysis simple the probability of dispersal from cell j to cell i, dij, is a by avoiding that additional movement mode. function of the distance between cells j and i and follows a normal probability distribution with parameters μ (mean displacement from cell j) and σ (stan- Adult survival dard deviation of the kernel, or the mean dispersal in one direction). The effects of variation in μ and σ on Post-recruitment individuals experienced age- and μ marine reserve design are well known for models of density-independent natural mortality A and fishing gonochore populations (e.g. White et al. 2010b), so mortality F as a function of age (F = 0 within any re- Easter & White: Spatial management for coastal protogynous sex-changing fishes 227

Table 2. Fixed model parameters and their values based on available data for serve). Fishing mortality F was repre- California sheephead Semicossyphus pulcher. See Alonzo & Mangel (2005) for sented in terms of the lifetime egg sources of parameter values production (LEP, calculated as the sum of the product of survival to age a Para- Parameter Definition and fecundity at age a over all ages) it meter value produced in the gonochore species, Larval dispersal/recruitment relative to the natural, unfished LEP μ 0 Mean larval displacement from cell i (fraction of LEP, FLEP), following σ 10, 100 km Standard deviation of the Gaussian dispersal kernel White et al. (2010a). The critical re- (mean dispersal in 1 direction) placement threshold (CRT), described as the minimum value of FLEP re- Growth quired for population persistence, was k 0.05 yr−1 von Bertalanffy growth rate parameterized so that CRT = 0.25 in all L∞ 90 cm von Bertalanffy asymptotic length model simulations. The level of fishing L 8 cm Larval size at recruitment 0 was expressed relative to the CRT, Population and results are comparable across −1 μA 0.35 yr Natural adult mortality species with similar LEP and CRT val- α 0.0001 Density-independent Beverton-Holt settler survival ues, allowing for descriptions of both β 1 Asymptotic Beverton-Holt maximum recruit density generic populations and real species CRT 0.25 Critical replacement threshold (minimum value of with empirically determined life his- fraction of unfished lifetime egg production required tory parameters (White & Rogers- for persistence) Bennett 2010, White et al. 2010a). For a given fishing scenario, we calculated Fishing r 1 cm Steepness of selectivity curve the relationship between F and FLEP in a non-spatial gonochore population Lf 20 cm Length at which there is a 50% chance a fish will be removed and then used that relationship to find the desired F for a specified FLEP in Reproduction the spatial model for use in all of the v 7.04 Constant in allometric fecundity relationship reproductive life histories. In the ab- w 2.95 Exponent in allometric fecundity relationship sence of reserves, the value of Fi in γ 1 Constant of fertilization function parameter each spatial cell was simply that value φ 1–20 Male importance; shape parameter in the fertilization F. When there were reserves, we function made the conservative assumption Gonochore that fishing effort inside reserves was LM 20 cm Length at which 50% of fish mature entirely reallocated outside of reserves, so that Ftotal = nF and the fish- Rule 1: fixed ing rate Fi in each non-reserve cell i Lc 30 cm Length at which 50% of fish change sex was Fi = F total/(1 − CR), where CR is the ρ 1 cm Shape parameter in the sex change function proportion of the coastline protected q 1 cm Shape parameter in the maturity function within the reserve. We took the approach of expressing F relative to Rule 2: relative size Δ gonochore FLEP because LEP is not Lc 14 cm Difference from the mean size at which pc(L) = 0.5 ρ 1 cm Shape parameter in the sex change function well suited to describing the effects of Δ fishing in a sex-changing fish, yet the LM 4 cm Difference from the mean size at which pM(L) = 0.5 FLEP approach is well suited for char- q 1 cm Shape parameter in the maturity function acterizing harvest rates relative to Rule 3: size frequency population persistence thresholds and Fc 0.67 Frequency of smaller mature individuals where is conceptually identical to the various pc(L) = 0.5 biological reference points used in ρ 50 Shape parameter in the sex change function fishery management (e.g. spawning FM 0.6 Frequency of smaller individuals at which pM(L) = 0.5 potential ratio, White et al. 2010a). q 50 Shape parameter in the maturity function Annual adult survival in each cell i was calculated from constant natural 228 Mar Ecol Prog Ser 543: 223–240, 2016

μ mortality A and size-specific fishing mortality Fi, (2012), because the former accounts for the greater where fishery harvest selectivity s(La) is given by: sperm contribution of larger males. We assumed that this biomass sex ratio was the operational sex ratio, 1 sL()a = (3) i.e. we did not consider the possibility of social hierar- []−−rL()a Lf 1e+ chies that could skew the operational sex ratio. We where r is the steepness of the selectivity curve, and further assumed male and female biomass have the

Lf is the length at which there is a 50% chance a fish same allometric relationship and the biomass sex ratio will be removed (cf. Alonzo & Mangel 2005). Then, Bt,i is male biomass divided by the sum of male and fe- σ annual adult survival i(La) in cell i is: male biomass. We assumed the proportion of fertilized eggs Pt,j could be described by a cumulative beta dis- [()]−μAi −FsL a σia()eL = . (4) tribution function with shape parameters γ and φ: γ φ Pt,j = beta(Bt,i, , ) (7) Growth and egg production where we assume γ is a constant set to 1, so the curve has negative concavity over its entire domain, and φ Growth in length followed a von Bertalanffy rela- is treated as a fertility parameter describing how tionship: quickly the proportion of eggs fertilized approaches 100% as B increases from zero (Fig. 1). This func- LL= 1e− −−ka() a0 (5) t,i a ∞ [] tional form describes a plausible relationship be- where La is the length at age a, L∞ is the asymptotic tween sex ratio and fertilization success (similar to maximum length, k is the growth rate, and a0 is the the relationship used in past models; e.g. Chan et al. effective age at length 0. Weight was an allometric 2012), with φ representing male importance: for φ = 1, function of length. We assumed that female fecundity fertilization increases linearly with sex ratio (males f(L) (the vector of eggs produced at each body length are very important, as in silversides), while for larger φ La) was proportional to mature female biomass, so values, e.g. = 20, the curve is saturating and asymp- each vector element f(La) was: totes near 100% fertilization with a low sex ratio (i.e. a very small number of males can fertilize all eggs, as fL()= p () L vLw (6) aMaa in bluehead wrasse; Fig. 1). where v and w are constants, and PM(La) is the probability of maturity (see below, ‘Maturation and sex change’). Maturation and sex change

We compared gonochoristic and 3 alternative pro- Mating function togynous sexual strategies using life history equations developed by Alonzo & Mangel (2005). In the gono- The contribution of males to reproductive output is poorly understood, and a general empirically based 1 allometric relationship between male body size and 0.9 sperm production does not exist (Alonzo & Mangel 0.8 2004), but presumably the probability of egg fertiliza- 0.7 tion is determined by the sex ratio. The only 2 such re- 0.6 lationships of which we are aware are for the 0.5 bluehead wrasse Thalassoma bifasciatum, in which a φ = 2 0.4 φ = 6 few males can effectively fertilize the eggs of hun- φ = 12 dreds of females (Warner et al. 1995, Petersen et al. 0.3 φ = 20 2001, Alonzo & Mangel 2004), and the inland silver- 0.2 sides Menidia beryllina, in which per-female produc- 0.1 Proportion of eggs fertilized tion of fertilized eggs increases linearly with the 0 proportional male sex ratio, suggesting a strong de - 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 pendence on the availability of males (S. M. Brander Sex ratio (proportional male biomass) et al. unpubl.). We assumed that fertilization de- Fig. 1. Example of the relationship between egg fertilization pended on the proportional male biomass Bt,i rather rate and sex ratio (proportional male biomass) for various than the numerical sex ratio, following Chan et al. levels of the male importance parameter, φ Easter & White: Spatial management for coastal protogynous sex-changing fishes 229

1 chore case, the sex ratio was assumed to be 0.5 (pro- pLMa()= (12) [(−−qSit, F M )] portion male biomass), and sex assignment was deter- 1e+ mined at birth. The timing of maturation as expressed where Si,t is the frequency of smaller mature individ- by pM (La), was determined by the absolute length of uals in cell i at time t and FM is the frequency at the individual: which the probability of maturing is 0.5, and 1 pLMa()= (8) 1e+ [(−−qLa LM )] 1 pLca()= (13) 1e+ [(−ρSFit, − c )] where LM is the length at which 50% of juveniles were anticipated to mature, and q determined the where Fc is the frequency at which 50% of the indi- steepness of the maturation probability function. viduals are expected to change sex. Note that the sex While similar previous studies of protogynous her- change parameters q and ρ take on different values maphrodites, including Heppell et al. (2006) and in the different sex change scenarios (Table 2). Chan et al. (2012), each considered just one protogynous mating function and sex change cue, we modeled one fixed and 2 flexible transition rules (rules 1, Spatial reserve scenarios 2, and 3, respectively, next paragraphs) for the timing of maturation pM(La) and sex change pc(La). We used Population persistence is essentially achieved equations from Alonzo & Mangel (2005) for pc(La). through replacement (each individual replaces itself Based on evidence from California sheephead that with ≥1 offspring during its lifetime), and both theo - the timing of maturity may also respond to changes reticalandempiricalresultssuggestthatpersistenceof in the size distribution in fished populations (Hamil- non-sex-changing metapopulations can be achieved ton et al. 2007), we applied the same functional forms through 2 processes: (1) network persistence, where to pM(La). persistence is achieved by replacement via larval Rule 1: fixed. Representing an endogenously cued exchange among all local populations, or (2) self- sex change function, the proportion of females ma- persistence, where individual local populations per- turing and transitioning to male was fixed, where the sist via sufficient retention of locally produced larvae probability of maturation pM(La) and the probability (Hastings & Botsford 2006, White et al. 2010b). Con- of sex change pc(La) were determined by the absolute sequently, spatial management with reserves that length of the individual (as in Eq. 8 for gonochores): support persistent populations can be achieved by either (1) having many small reserves, all well con- 1 pLca()= (9) nected by larval dispersal and with the fraction of [(−ρLLac − )] 1e+ coastline in reserves greater than or equal to the CRT where Lc is the size at which 50% of mature females required for persistence in non-spatial management change sex. The equation for pM(La) is identical, with (network persistence), or (2) having one or more indi- parameter q in the place of parameter ρ. vidual reserves large enough to retain a proportion of Rule 2: relative size. The probability of maturation locally produced larvae greater than or equal to the and sex change was determined by the mean length CRT (self-persistence; White et al. 2010b, 2011). Fol- of all individuals in the cell: lowing the example of earlier studies (e.g. Moffitt et al. 2013), we simulated results for both network- 1 pLMa()= (10) persistent reserve systems and self-persistent reserve [(−−qLa ( LiM+Δ L ))] 1e+ systems, with the understanding that those 2 sce - Δ where LM is the difference from the population narios define the extremes of a continuum of possi- mean length at which the probability of an individual ble reserve configurations (many small vs. few large) maturing is 50%, and Li is the mean length of all indi- in a spatial management plan. viduals in cell i. Then

1 pLca()= (11) Model analysis: Population persistence thresholds 1e+ [(−ρLLa − (i +Δ Lc ))] Δ where Lc is the difference from the mean at which Our primary objective was to determine how the the probability of sex change is 0.5. reduction in sex ratio due to fishing affects the mini- Rule 3: size frequency. The probability of matura- mum reserve requirements (reserve size or total tion and sex change was determined by the fre quen- reserve area) for sustaining persistent protogynous cy of smaller mature individuals at the mating site: hermaphrodite populations. Because we expressed 230 Mar Ecol Prog Ser 543: 223–240, 2016

fishing rates in terms of FLEP, our calculations of per- gated the influence of fishery management outside sistence thresholds are insensitive to the particular reserve boundaries on the reserve requirements for values chosen for most demographic parameters population persistence (CR and WR). Specifically, we shared by gonochoristic and sex-changing species analyzed the role of fishery size limits by varying the

(e.g. length at age, natural mortality rate; White et al. mean size of entry to the fishery (Lf) from the baseline 2010a,b). However, several life history features value, the mean size at maturity in the gonochore unique to hermaphroditic species are not captured population (20 cm, reflecting the common goal of by FLEP: (1) the cue triggering sex change (fixed allowing fish to reproduce before harvest), up to the size, relative size, or size frequency); (2) φ, the param- mean size at sex change in an unfished protogynous eter describing the relationship between sex ratio population (30 cm, reflecting the parallel goal of and fertilization success; and (3) the size of recruit- allowing fish to change sex before harvest). Although ment to the fishery (Lf) relative to the size at which there is no fishing inside the reserve, it is reasonable sex change occurs. Therefore, we determined how to expect that changing fishery management outside each of those life history attributes affected minimum reserves to target either one or both sexes could shift reserve requirements for population persistence. the dynamics of the system. When changing Lf, we We first characterized the general effects of φ and recalculated the relationship between F and gono- sex change cue on population dynamics by varying chore FLEP before determining the F used in simula- the level of fishing effort, simulating scenarios rang- tions. This describes a realistic scenario where in - ing from sustainably fished (F equivalent to gono- creasing the length limit increases the intensity of chore FLEP = 0.3 in fished areas; this is greater than fishing on larger fish, rather than reducing overall the CRT of 0.25, so reserves are not necessary for effort (Cox & Walters 2002). gonochore population persistence) down to severely When estimating the minimum values of CR and WR, overharvested (F equivalent to FLEP = 0 in fished ar- we calculated persistence in 2 ways: (1) scorched eas). Note that in all of these cases, F is calculated to earth, where no reproduction occurred outside of re- give the corresponding FLEP in the non-spatial, no- serve boundaries (i.e. FLEP = 0 in fished areas; this is reserve case. As reserve area increases and fishing a conservative approach that assures reserves are in- effort is redistributed, Ftotal remains the same but Fi in dependent of conditions beyond their boundaries and each cell increases, and the realized FLEP is lower was achieved by simply setting reproduction to zero than the target. In these initial simulations, we chose outside of reserves), and (2) a more realistic scenario reserve scenarios that would allow either self- in which the exploited population outside of the re- persistence or network persistence in the gonochore serves was achieving some reproduction (but less population (see next 2 sections below for descriptions than the CRT; FLEP = 0.2) and contributing recruits to of each scenario). the metapopulation. In the following paragraphs, we We then found the minimum fraction of coastline in describe how we made these calculations for network- reserve CR that allowed network persistence among persistent and self-persistent reserve scenarios. many small reserves or the minimum reserve width

WR that allowed self-persistence within a single large reserve. We made this calculation using the baseline Network persistence life history parameters for each of the 3 sex change modes (plus gonochores), varying male importance To simulate a network-persistence scenario, we from very low (φ = 20) to extremely high (φ = 2). Our held WR (the width of an individual reserve) small model differs from that of Heppell et al. (2006) and enough relative to the larval dispersal distance so

Chan et al. (2012), who considered only 2 mating that self-persistence was not possible (σ = 100, WR = functions (i.e. male importance values) that fall 0.1σ). We then varied the fraction of the coastline roughly in the middle of our range. We investigated a protected within reserve, CR, from 0 (no reserve) to 1 wider range of possible mating function shapes, in - (complete protection) to determine what minimum cluding extremely low values of φ that actually corre- fraction of the coastline CR was required for popula- spond to the nearly linear mating function observed tion persistence. Note that this required varying the in inland silversides M. beryllina (S. M. Brander et al. size of the coastline, n, to accommodate different CR unpubl.). values for a constant WR, but because the coastline is Spatial management can also involve coordination circular, this did not create an artifact in the results. between reserves and fishery regulations outside of The criterion for network persistence is calculated by those reserves. Therefore, we additionally investi- first estimating eggs per recruit (EPR), the number Easter & White: Spatial management for coastal protogynous sex-changing fishes 231

of eggs produced by a new recruit over its lifetime While sheephead demographics were used in the when the population is at equilibrium. For sex- model, it is important to note that model results are changing scenarios, we estimated this value using not limited to this species and, rather, are dependent the equilibrium values of the length-dependent on the shape of the fertilization success curve, which prob ability of sex change and fertilization success. we parameterized to capture a range of possible fer- We then generated an egg production matrix C by tilization patterns, and the factors cueing sex change, multiplying each row of the dispersal matrix D by which are generally less studied than the growth, the value of EPR for the corresponding spatial cell. survival, and reproduction of protogynous species.

The elements cij of C then give the total number of We normalized model outputs by expressing biomass eggs per recruit produced in j that disperse to i. This as a proportion relative to the biomass of an unfished λ matrix has dominant eigenvalue C, and network gonochore population. αλ ≥ α persistence requires that C 1, where is the slope of the Beverton-Holt function at the origin (White 2010). In other words, each recruit must RESULTS replace itself within the metapopulation within its lifetime (Hastings & Botsford 2006). Previous work General patterns of protogynous population has shown that gonochores achieve network persist- dynamics in reserves ence in the scorched earth scenario when CR ≥ CRT (White et al. 2010b), i.e. 25% in our model. The general effects of fishing on protogynous hermaphrodites in our model matched our expectations from the non-spatial models of Alonzo & Mangel Self-persistence (2004). For a moderate value of male importance (φ =

6) and the baseline size at entry to the fishery (Lf = To simulate the self-persistence scenario, we held 20 cm), a high but sustainable (without reserves) rate

CR below the level needed for network persistence (CR of size-selective fishing (FLEP = 0.30) reduced bio- ≥ 0.25 is needed for persistence given the CRT, so we mass and perturbed the sex ratio in fished areas, chose CR = 0.1 for these simulations), imposed a while inside reserves biomass remained high and sex shorter dispersal distance (σ = 10), and varied WR (as a ratios remained similar to those of unexploited pro- proportion of σ) to determine the size of an individual togynous populations (numerical sex ratio of ~34% reserve required for self-persistence. For these simu- male for fixed size and relative size strategies and lations, we again varied n so that CR remained con- ~27% male for the size frequency strategy). This stant as WR increased relative to σ. Self-persistence general pattern held for both network-persistence was determined in the same manner described above scenarios (i.e. CR = 0.25, WR = 0.1σ; Fig. 2a,b) and for network persistence, but only the submatrix of the self-persistence scenarios (i.e. CR = 0.1, WR = σ; connectivity matrix C corresponding to the cells results not shown). Although sex ratios were reduced within the reserve was included. Gonochores are ex- outside of the reserve for all protogynous cases, the pected to be self-persistent in reserves when WR ≥σ effect of fishing differed between the sex change sce- (larval dispersal distance) if CRT = 0.35 (Botsford et al. narios. The fixed-cued protogynous population was 2001, White et al. 2010b) but may persist in a smaller the most sensitive to fishing, had the lowest equilib- reserve if the CRT is smaller or if the FLEP is greater rium biomass (Fig. 2a) and the lowest equilibrium sex than zero outside reserves (White et al. 2010b). ratio outside of the reserve (<7% male; Fig. 2b), and exhibited the greatest difference in sex ratio between the protected and harvested zones, reflecting the Model parameterization inability to compensate for the disproportionate loss of males by early maturation and sexual transition. Baseline parameter values were taken from Alonzo The relative size-cued population sustained higher & Mangel (2005) and based on previous research biomass (just greater than that of the gonochore) (Warner 1975, Cowen 1985, 1990) on California under the same fishing rate (Fig. 2a) and maintained sheephead Semicossyphus pulcher (Labridae), a more males in fished areas (nearly 10% male; commercially and recreationally important proto - Fig. 2b), as individuals were able to shift the timing of gynous hermaphrodite wrasse that is common in the maturation and sex change to earlier ages in rocky reefs and kelp forests of southern California, response to size-selective (and thus sex-selective) USA. Parameter values are reported in Table 2. harvest. The size frequency-cued population showed 232 Mar Ecol Prog Ser 543: 223–240, 2016

Sustainable fishing (FLEP = 0.3) 1 ab1 Gonochore Fixed 0.8 0.8 Relative size Size frequency

0.6 0.6

0.4 0.4

0.2 ratioSex (prop. male) 0.2 Biomass unfished) to (relative 0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Distance along coastline (km) Distance along coastline (km) Unsustainable overfishing (FLEP = 0.15) 1 cd1

0.8 0.8

0.6 0.6

0.4 0.4

0.2 ratioSex (prop. male) 0.2 Biomass unfished) to (relative 0 0 0 20406080100120 0 20 40 60 80 100 120 Distance along coastline (km) Distance along coastline (km)

Fig. 2. (a,c) Population biomass (expressed as a proportion of unfished biomass) and (b,d) sex ratio (% male) of populations with different life histories along a coastline with marine reserves. The figure shows a segment of the infinite (circular) coastline con- taining no-take reserves that cover CR = 25% of the coastline; each reserve has width equal to 10% of the larval dispersal distance, so network persistence is possible but self-persistence is not. The non-reserve area was fished at a harvest rate that was either (a,b) sustainable without reserves (equivalent to FLEP = 0.3) or (b,c) unsustainable without reserves (equivalent to FLEP = 0.2). Protogynous populations (with fixed, relative size, or size frequency cues, indicated by line type) had intermediate male importance (φ = 6) a more consistent sex ratio along the length of the the network scenario (Fig. 2c). Those 2 sex change coastline than fixed size- and relative size-cued pop- cues also exhibited even greater reductions in sex ulations, did not experience a dramatically reduced ratio in fished areas (<5% male). Interestingly, these male population in the fished areas (Fig. 2b), and populations had a greater proportion of males within actually sustained higher equilibrium biomass than the reserve (~34 to 38% male; Fig. 2d) than in the less the gonochore along the entire coastline (Fig. 2a). fished scenario (≤34%; Fig. 2b). This increased sex The differences among reproductive strategies ratio is likely an effect of the population being closer became more evident when fishing was intense to collapse: very few larvae are spawned outside of enough to cause the population to collapse in the the reserve, so recruitment is lower along the entire absence of reserves (FLEP = 0.15). With that level of coast (including inside the reserve) than in scenarios fishing, fixed size- and relative size-cued protogy- with less fishing. However, larvae that do settle in the nous populations exhibited drastically depleted pop- reserve have a long lifespan, resulting in a large ulations, with the fixed size population near zero in number of old, large males there. This combination of Easter & White: Spatial management for coastal protogynous sex-changing fishes 233

factors produces a shifted age structure (towards the once again higher biomass than the gonochores older, predominantly male age classes) within the along the entire coastline (Fig. 2c). reserve, relative to scenarios with less fishing and The differing responses to fishing of the 4 repro- higher larval recruitment. However, this effect did ductive strategies can be summarized by examining not materialize in the size frequency-cued popula- the coast-wide average biomass and sex ratio (Fig. 3; tion, which maintained sex ratios similar to those of nearly identical results for the self-persistence simu- the less fished population (Fig. 2b), with a substan- lations are not shown). For the moderate level of male tially greater sex ratio (20% male) in fished areas and importance (φ = 6) shown in Fig. 2, biomass decreases

Low male importance (φ = 20) 1 1 Gonochore a b Fixed Relative size 0.8 0.8 Size frequency 0.6 0.6

0.4 0.4

0.2 0.2

0 0 0 0.1 0.2 0.3 0 0.1 0.2 0.3

Moderate male importance (φ = 6)

1 c 1 d 0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2

0 0 0 0.1 0.2 0.3 0 0.1 0.2 0.3 Biomass unfished) to (relative Sex ratioSex in reserve (prop. male)

High male importance (φ = 2) 1 e 1 f 0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2

0 0 0 0.1 0.2 0.3 0 0.1 0.2 0.3 (more (less fishing) Fraction of lifetime egg production (FLEP) fishing) Fig. 3. (a,c,e) Population biomass (expressed as a proportion of unfished biomass) and (b,d,f) sex ratio (% male) of populations with different life histories along a coastline with marine reserves and varying intensity of fishing. The coastline contains no- take reserves that cover CR = 25% of the coastline; each reserve has width equal to 10% of the larval dispersal distance, so network persistence is possible but self-persistence is not (as in Fig. 2). The fishing rate in non-reserve areas was equivalent to the indicated gonochore FLEP; FLEP < 0.25 results in gonochore population collapse without reserves. Protogynous populations (with fixed size, relative size, or size frequency cues, indicated by line type) had (a,b) low; (c,d) intermediate; or (e,f) high male importance (indicated by the mating function parameter φ) 234 Mar Ecol Prog Ser 543: 223–240, 2016

faster with increased fishing for the fixed size- and mediate reserve requirements that fell between the relative size-cued protogynous populations, while the relative size-cued and the gonochore populations size frequency-cued population responded similarly (Fig. 4). In this scorched earth scenario, protogynous to the gonochore population (Fig. 3c). The sex ratio populations always required more protection than the inside reserves also increased as FLEP decreased (i.e. gonochores. This is because in gonochore populations, fishing increased) for the fixed size- and relative size- large, old female fish accumulate in reserves, and cued populations, reflecting the increase within re- their large size corresponds to very high egg produc- serves seen in the spatial distribution (Fig. 2). tion. In a protogynous species, the large fish that ac- The value of the male importance parameter, φ, cumulate in reserves are predominantly males, which had a strong influence on population dynamics. In do not contribute to an exponential increase in egg general, when males were more important to fertil- production in the same way that large females do ization success (smaller values of φ), the loss of males (once the biomass sex ratio is sufficiently high for most in fished areas had a more severe effect on reproduc- eggs to be fertilized). Under scorched-earth conditions, tion. The relative size-cued and especially the fixed all fish are assumed to be harvested prior to spawning size-cued population collapsed more rapidly with outside the reserves, so we do not consider the effects increased fishing (Fig. 3e), with sex ratios that were of size limit regulations. skewed heavily towards females in harvested zones and towards males in reserves (Fig. 3f). In contrast, if 0.7 a Gonochore very few males were required for fertilization (e.g. Fixed 0.6 Relative size φ = 20), the protogynous populations declined much Size frequency ) more gradually with increased fishing (Fig. 3a), and R 0.5 the reserve sex ratio only increased at very high fish- C ing rates for the fixed size- and relative size-cued 0.4 populations (Fig. 3b). The latter occurred because 0.3 male depletion in fished areas had a smaller effect on overall reproductive output and consequent age 0.2 structure (and sex ratio) shift. within reserve ( 0.1 Minimum fractionMinimum coastline of 0 Thresholds for population persistence under 1 3 579 11 13 15 17 19 spatial management 3.0 b

Scorched earth: No reproduction outside reserves ) R 2.5 W As the patterns in Figs. 2 & 3 suggest, differences in 2.0 reserve protection requirements between gonochore and protogynous hermaphrodite populations de- 1.5 pended on both sex change cue and the parameter describing male importance, φ. The protogynous 1.0 populations with fixed size- and relative size-cued sex change required substantial protection to persist 0.5 when males were of greatest importance (φ = 1) and Minimum reserveMinimum ( width

no reproduction was occurring outside of the reserve (prop. of larval dispersal distance) 0.0 (up to 55% of the coastline or a reserve >1.7 times 1 3 579 11 13 15 17 19 the dispersal distance; Fig. 4). The level of protection High Male importance (φ) Low required for these populations to persist quickly Fig. 4. (a) Minimum fraction of the coastline within reserve, dropped as males became less important; however, CR, to achieve network persistence or (b) minimum reserve both fixed size- and relative size-cued populations width, WR (as a proportion of larval dispersal distance), to still had greater persistence thresholds (CR > 0.35 or achieve self-persistence as a function of male importance (mating function parameter φ) for populations with different WR ≥ dispersal distance) than the gonochore and the reproductive life histories (indicated by line type). This sce- size frequency-cued population, even when very few nario represents scorched earth, where harvest was suffi- males were required for fertilization success. The size ciently intense that no reproduction occurred outside of the frequency-cued protogynous population had inter - reserve (FLEP = 0) Easter & White: Spatial management for coastal protogynous sex-changing fishes 235

Some reproduction outside reserves ios) for all of the life histories (Fig. 5a,b). In fact, as males became less important (larger φ), the protogy- Allowing the exploited population outside of the nous populations no longer needed reserves to per- reserves to achieve some reproduction (FLEP = 0.2) sist in this scenario, unlike the gonochores. The under the baseline fishery size limit (Lf = 20 cm) reserve area and size requirements declined faster resulted in lower network and self-persistence with φ for the 2 more flexible sex change cues thresholds (compared to the scorched earth scenar- (Fig. 5a,b).

0.7 a 3.0 b Lf = 20 cm Gonochore 0.6 2.5 Fixed Relative size 0.5 Size frequency 2.0 0.4 1.5 0.3 1.0 0.2

0.1 0.5

0 0.0 1 3 579 11 13 15 17 19 1 3 579 11 13 15 17 19 L = 25 cm 3.0 0.7 c f d ) R

0.6 W 2.5 ) R

C 0.5 2.0 0.4 1.5 0.3 1.0 0.2 within reserve ( 0.1 0.5 Minimum reserveMinimum ( width Minimum fractionMinimum coastline of 0 0.0 1 3 579 11 13 15 17 19 (prop. of larval dispersal distance) 1 3 579 11 13 15 17 19 0.7 3.0 e Lf = 30 cm f 0.6 2.5 0.5 2.0 0.4 1.5 0.3 1.0 0.2

0.1 0.5

0 0.0 1 3 579 11 13 15 17 19 1 3 579 11 13 15 17 19 High Male importance (φ) Low High Male importance (φ) Low

Fig. 5. (a,c,e) Minimum fraction of the coastline within reserve, CR, to achieve network persistence or (b,d,f) minimum reserve width, WR (as a proportion of larval dispersal distance), to achieve self-persistence as a function of male importance (mating function parameter φ) for populations with different reproductive life histories (indicated by line type). In this scenario, fishing is unsustainable (persistence is not possible without a reserve for the gonochore) but less intense than scorched earth (FLEP = 0.2). The minimum harvest size limit in fished areas was (a,b) 20 cm (equivalent to unfished size at maturity); (c,d) 25 cm; or (e,f) 30 cm (equivalent to unfished size at sex change) 236 Mar Ecol Prog Ser 543: 223–240, 2016

Fishery regulations outside marine reserves centrated on predominantly male size classes. (4) Importantly, our simulations also revealed that sex Population persistence thresholds when there was ratios within reserves may not be informative met- reproduction outside reserves (FLEP = 0.2) changed rics of reserve performance for protogynous species. substantially when the minimum size limit of the fish- Although our model was constructed using para- ery was increased from 20 to 25 or 30 cm (Fig. 5c−f). meter values for a particular species, and thus spe- Essentially, for larger minimum size limits, the per- cific details in our results may not apply exactly to all sistence thresholds for the 2 protogynous populations protogynous stocks, it is important to note that major with less flexible sex change (fixed size and relative differences in our model results were due to variation size) became more similar to those of the scorched in the sex change cue and value of male importance earth scenario. This shift in persistence requirements (φ) only. Thus, similar to the conclusions of Alonzo & occurred because increasing the minimum size limit Mangel (2005), Huntsman & Schaaf (1994), and Hep- of the fishery concentrated all of the fishing effort on pell et al. (2006), our work confirms that simply the larger sizes, thus removing a larger proportion of knowing that a species exhibits protogyny and that the males from the population. Consequently, there males are disproportionately removed by fishing is were too few males to contribute to reproduction out- necessary but not sufficient to predict how that pop- side reserves (particularly when the sex change cue ulation will respond to fishing pressure or how best to was fixed), even for very low levels of the male design spatial management for that stock. However, importance parameter. Note that the persistence we also addressed a second major factor affecting the requirements for the size frequency-cued and gono- response of protogynous species to size-selective chore populations were not affected by the change in harvest: When does the loss of males become a con- fishery size limits (Fig. 5c−f). cern (Rankin & Kokko 2007)?

DISCUSSION Importance of the mating function

We used a spatially explicit model of a generic Our work builds on previous studies of protogy - species to determine how spatial management nous hermaphrodite population dynamics (Alonzo & guidelines should be adjusted to ensure population Mangel 2005, Heppell et al. 2006, Chan et al. 2012) persistence in protogynous hermaphroditic fishes. by simulating a range of spatial management sce- Our simulations confirmed that protogynous stocks narios and sex change functions and further consid- cannot always be managed similarly to gonochore ering the contribution of males to reproductive suc- populations (Huntsman & Schaaf 1994, Alonzo & cess. However, unlike our finding that population Mangel 2004, 2005, Heppell et al. 2006, Alonzo et persistence within reserves depended strongly on al. 2008, Chan et al. 2012) and may require either the level of male importance (i.e. the concavity of greater or less protection in marine reserves than the mating function), Chan et al. (2012) found that gonochores to ensure population persistence, the effects of reserves were generally similar among depending on their specific life history traits. The the 2 mating functions (i.e. male importance value) main new results emerging from our analysis were they considered. We investigated a wider range of as follows. (1) The necessary level of reserve protec- possible mating function shapes, from scenarios tion required for persistence of protogynous popula- where very many to very few males are required to tions depended strongly on the relationship achieve high levels of fertilization, and also exam- between the sex ratio and fertilization success (the ined more than one sex change strategy. Thus, we mating function), which is empirically unknown for likely captured a fuller range of biologically plausi- most fishes (Alonzo & Mangel 2005, Heppell et al. ble results for real species. In particular, the low 2006). (2) The nature of the cue triggering sex values of φ that produced extreme results in our change also affected reserve requirements, where simulations actually correspond to the nearly linear species with less flexible sex change cues required mating function observed in inland silversides more or larger reserves. (3) The size of reserves Menidia beryllina (S. M. Brander et al. unpubl.), required by those less flexible populations was also whereas the 2 mating function shapes considered more sensitive to changes in the minimum harvest by Chan et al. (2012) would both fall in the middle size limits for the fishery outside reserve boundaries, of the distribution of values we used. Given the requiring more protection when fishing was con- importance of the mating function on spatial man- Easter & White: Spatial management for coastal protogynous sex-changing fishes 237

agement in our simulations, we recommend greater Caribbean parrotfishes (family Scaridae) at the most focus on the empirical determination of fertilization heavily fished islands may have been failing to rates and mating functions. reproduce due to a lack of terminal-phase males and suggested that those populations were dependent on larval dispersal from elsewhere. Because it is thought Effects of fishery management on reserve that many protogynous species respond to localized performance spawning cues from males, heavy exploitation of males has the potential to cause females to go Our results indicated that even with marine unspawned (male limitation), reduce fertilization as reserves in place, it is important for spatial manage- males try to appropriate sperm among a large num- ment strategies to consider the influence of fishery ber of females (sperm limitation), or lead to large- management outside of the protected zones. Our scale reproductive failure (Coleman et al. 1996). results indicated that if protogynous populations are Thus, scorched earth may be a more realistic possi- heavily exploited outside of reserves (such that bility for overexploited protogynous species, espe- reproduction is greatly reduced), persistence will cially migratory ones, than it is for gonochores, require more reserves or larger reserves than those where that assumption has been criticized (White et required by gonochores. Alternatively, if fishing is al. 2010b). less intense so that there is some reproduction occurring outside reserves, protogynous species can have lower protection requirements than gonochores and Implications for monitoring and adaptive may not require reserves for persistence at all. That management result depends on the mating function (as males become less important, reserve requirements drop) In addition to predicting the effect of different life and on fishery size regulations: when the minimum histories and fishery regulations on marine reserve size limit was higher and the fishery concentrated on requirements to achieve population persistence, our larger size classes, the populations with less flexible simulations identified considerations that must be sex change rules required more or larger reserves. taken in empirical assessments of how well reserves This is because the fishery primarily removes males are meeting specific goals. Often, after:before or (particularly when the population cannot respond by inside:outside ratios of key metrics (such as biomass) adjusting the sex ratio), depleting the sex ratio and are used to assess the effectiveness of marine impairing reproduction outside reserves. Note that reserves (White et al. 2011), although Moffitt et al. this result was obtained because we assumed that (2013) recently showed that inside:outside biomass higher minimum size limits were associated with ratios are not reliable indicators of reserve success. In higher fishing mortality rates, so that the gonochore the case of protogynous hermaphrodite stocks, eval- FLEP was the same regardless of the size limit (i.e. uations have increasingly focused on the difference the size limit is a catch control, not an effort restric- in sex ratio after:before or inside:outside reserves tion). If instead we had assumed that raising the size (e.g. Beets & Friedlander 1999, Adams et al. 2000, limit simply removed fishing effort on smaller size Hawkins & Roberts 2004, Kleczkowski et al. 2008). classes, we would have found a relaxation in persist- Our simulations showed that empirical assessments ence re quirements. Nonetheless, our results do sug- may actually detect a greater proportion of large, old gest that spatial management of protogynous fishes males within reserves when population biomass is should take into consideration the possibly counter- severely depleted and the population is only persist- intuitive effects of minimum size limits that may con- ent because of reserve protection. In contrast, scenar- centrate effort on males rather than spreading it ios with lower exploitation rates and higher biomass across both sexes. However, one factor we did not that could support sustainable populations without account for is the potential for different fisheries with reserves may have smaller inside:outside differences different size targets (e.g. plate size vs. trophy fish- in sex ratio. Consequently, the inside:outside differing) in protogynous species with extreme sexual ence in sex ratio is not necessarily a reliable indicator dimorphism, such as the California sheephead. of population health or fishery sustainability. It has While our scorched earth scenario represents a been noted that changes in total biomass might not hypothetical extreme, evidence of reproductive fail- reflect the population stability of protogynous her- ure in protogynous stocks has been documented. For maphrodites, as the disproportionate removal of example, Hawkins & Roberts (2004) noted that some males may reduce fertilization rates while female 238 Mar Ecol Prog Ser 543: 223–240, 2016

biomass or egg production remain unaffected (Punt reserves, reserves would generally be expected to et al. 1993, Alonzo & Mangel 2004). The opposite improve yield (Neubert 2003, Neubert & Herrera may occur in reserves, as males will accumulate in- 2008, White et al. 2008, 2010a, Moeller & Neubert side reserves (supposedly indicating reserve success) 2013). Fishery yield would likely be optimized for even if the reserves are too small or too few to ensure some combination of reserve size, harvester behav- population persistence, and the loss of recruits to ior, and (lower) exploitation rate that we did not con- unprotected areas results in overall lower reproduc- sider in our study (White et al. 2008). tive output and population decline. Because of these Finally, our study focused on the ecological aspects potential effects, managers must exercise caution of fishing and did not consider the possible role of when using increases in total or male biomass to fishery-induced evolution on protogynous species reflect population recovery. (Law 2000). For example, fishery-induced shifts in the size at maturity and sex change have been re - ported for California sheephead S. pulcher (Hamilton Model limitations et al. 2007). In that case, it is not possible to tell whether the shifts were plastic responses to fishing While we have shown that spatial management of pressure (such as would occur in our model) or long- protogynous fishes could be improved with knowl- term evolutionary changes. In the latter case, re - edge of the mating function and ecological cues trig- serves could have the additional benefit (not in - gering maturation and sex change, we acknowledge cluded in our model) of potentially rescuing the that this information is not available for many species population from fishery-induced selection (Dunlop et (particularly the mating function). In data-limited sit- al. 2009), although protogynous species have not yet uations, a simpler framework that does not require a been specifically examined in eco-evolutionary fish- mating function, such as the per-recruit model used ery models. by Grüss et al. (2014), could be used. Nonetheless, our results show that management would benefit from utilizing that information if it is available. Addi- CONCLUSIONS tionally, our work specifically focused on coastal protogynous species rather than those that undertake Overall, our findings indicate that the interaction migrations to offshore spawning habitats (such as between biological factors (sex change cue and mat- gag grouper Mycteroperca microlepis). There has ing function) and fishery management determines been recent work developing spatial management whether and how marine reserve designs must be guidelines for gonochore species with ontogenetic or adjusted to accommodate protogynous life histories. spawning migrations (White 2015), so extending that Under the most conservative assumptions about work to migratory protogynous species could be a reproduction outside reserves, protogynous species valuable next step. always required more or larger reserves than gono- As the focus of our study was largely on the biology chores. However, under the potentially more likely (i.e. the cues for maturation and sex change and mat- scenario that there is reproduction outside reserves, ing function) rather than the economics of coastal protogynous species required more or larger re - protogynous fisheries, our analysis centered on pop- serves than gonochores when males became limit- ulation persistence, not yield, and included the some- ing, either because the mating function was less con- what simplistic assumption that total fishing effort cave or because minimum size limits concentrated was held constant following the introduction of fishing on predominantly male size classes. When reserves. However, fishing effort may respond dy - males were less important or fishing was spread namically to reserve implementation (Sanchirico & among males and females, protogynous species re- Wilen 2001), and reserve success can be affected by quired less protection than gonochores (particularly harvester behavior (e.g. Kellner et al. 2007). It is for species with more flexible sex change cues). The important to note that we focused on population per- 2 spatial dispersal scenarios we modeled (self-persis- sistence, because spatial management using re - tence and network persistence) produced similar serves is frequently concerned with identifying re- results, indicating that our general findings are not serve configurations that will sustain populations strongly affected by the details of larval connectivity. regardless of management outside the reserves (e.g. In addition, our work indicates that conventional Botsford et al. 2001). For the scenarios we modeled in metrics (such as sex ratio) used in evaluating the effi- which the fishery would be overharvested without cacy of marine reserves may not accurately reflect Easter & White: Spatial management for coastal protogynous sex-changing fishes 239

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Editorial responsibility: Romuald Lipcius, Submitted: April 30, 2015; Accepted: November 29, 2015 Gloucester Point, Virginia, USA Proofs received from author(s): January 22, 2016