Catastrophic Mortality, Allee Effects, and Marine Protected Areas

vol. 193, no. 3 the american naturalist march 2019

Emilius A. Aalto,1,* Fiorenza Micheli,1 Charles A. Boch,1,2 Jose A. Espinoza Montes,3 C. Broch Woodson,4 andGiulioA.DeLeo1

1. Hopkins Marine Station, Stanford University, Pacific Grove, California 93950; 2. Monterey Bay Aquarium Research Institute, Moss Landing, California 95039; 3. Sociedad Cooperativa de Produccion Pesquera Buzos y Pescadores, Isla Natividad, Baja California Sur, Mexico; 4. University of Georgia, Athens, Georgia 30602 Submitted December 8, 2017; Accepted September 8, 2018; Electronically published February 1, 2019 Online enhancements: appendixes. abstract: For many species, reproductive failure may occur if abun- Lubchenco2008).DefaunationintheAnthropocenehasbeen dance drops below critical Allee thresholds for successful breeding, in extensively documented in both terrestrial (Dirzo et al. 2014) some cases impeding recovery. At the same time, extreme environmen- and marine (McCauley et al. 2015) environments as a conse- tal events can cause catastrophic collapse in otherwise healthy popula- quence of land-use change, pollution, and overharvesting. tions. Understanding what natural processes and management strategies Forspeciesthat experienceAllee effects—that is,lower breed- may allow for persistence and recovery ofnatural populations is criticalin ing success at low densities (Allee 1932)—a period of height- the face of expected climate change scenarios of increased environmental ened mortality can reduce abundance to a level that threatens variability. Using a spatially explicit continuous-size fishery model with stochastic dispersal parameterized for abalone—a harvested species with recovery (Gascoigne and Lipcius 2004). The most dramatic sedentary adults and a dispersing larval phase—we investigated whether consequence of Allee effects is the negative per capita popula- the establishment of a system of marine protected areas (MPAs) can pre- tion growth when a population drops below a critical density vent population collapse, compared with nonspatial management when threshold, further lowering abundance and growth in a neg- populations are affected by mass mortality from environmental shocks ative feedback loop or “extinction vortex” (Gilpin and Soulé and subject to Allee effects. We found that MPA networks dramatically 1986; Fagan and Holmes 2005). This risk is exacerbated for – reduced the risk of collapse following catastrophic events (75% 90% harvestedspeciesand,inparticular,fisheries,asexploitedpop- mortality), while populations often continued to decline in the absence fi of spatial protection. Similar resilience could be achieved by closing the ulations are typically maintained at arti cially low densities fishery immediately following mass mortalities but would necessitate even when carefully managed to guarantee long-term, maxi- long periods without catch and therefore economic income. For species mumsustainableyield(MSY).Thecombinationofnaturalen- with Allee effects, the use of protected areas can ensure persistence fol- vironmental variability and anthropogenic pressure increases lowing mass mortality events while maintaining ecosystem services dur- the likelihood that harvested populations drop below the den- ing the recovery period. sityatwhichbreedingsuccessdiminishes,makingsuchspecies Keywords: catastrophe, marine reserves, fishery management, marine particularly vulnerable to Allee effects (Berec et al. 2007). In protected area (MPA), abalone, recruitment failure, resilience, marine addition to slowing or preventing recovery in exploited spe- populations, environmental shocks. cies, Allee effects increase uncertainty and may amplify the effects of demographic stochasticity, environmental variability, and harvest-induced cycling (Fryxell et al. 2010; Kupari- Introduction nen et al. 2014). The risk of reproductive failure in exploited fi Understanding, quantifying, and improving resilience of wild populations may further increase when harvesting speci - populations to natural and anthropogenic disturbance is a cally targets population aggregations (Sadovy and Domeier central problem in ecology, conservation biology, and natu- 2005), males (Petersen and Levitan 2001), or large spawners ral resource management (Dunham et al. 1999; Levin and (De Leo and Micheli 2015). A drop in fertilization success at low population density has been extensively documented in marine environments * Corresponding author; email: [email protected]. for broadcast spawners and observed in several harvested ORCIDs: Aalto, https://orcid.org/0000-0001-8705-1000; Woodson, https:// orcid.org/0000-0003-1325-3667. benthic invertebrates, including queen conch (Stoner et al. Am. Nat. 2019. Vol. 193, pp. 000–000. q 2019 by The University of Chicago. 2012), sea urchin (Levitan et al. 1992), and abalone (Babcock 0003-0147/2019/19303-58129$15.00. All rights reserved. et al. 1999; Hobday et al. 2000). Other marine exampleschar- DOI: 10.1086/701781 acterized by Allee effect at low population density include

This content downloaded from 171.066.209.130 on February 05, 2019 15:37:11 PM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). 000 The American Naturalist vertebrates such as herring (Saha et al. 2013), cod, and pol- (Hutchings and Reynolds 2004). Even when recovery is pos- lock (Keith and Hutchings 2012). Terrestrial examples of sible, fishing closure may be economically and socially un- harvested species that experience Allee effects are rarer than sustainable if recovery is slow and requires a prolonged mul- in the ocean but include elephants (Dobson and Poole 1998) tiyear closure, causing a significant loss of catch and income and plants such as wild ginseng (Hackney and McGraw and, ultimately, the possible collapse of the entire business 2008).Maintaining viable breeding densities for such species sector (e.g., sardines in Monterey [Radovich 1982] and cod isachallenge,asthecollapseforexploitedspeciesisoftenpla- inNewfoundland[Myersetal.1997]).Alternatively,thefish- teau shaped, meaning that it may occur suddenly without ery can be managed by setting harvesting effort below that early-warning signals of decline (Mullon et al. 2005; Boetti- at MSY, decreasing fishing mortality and maintaining pop- ger and Hastings 2013), and is therefore difficult to antici- ulation well above the Allee threshold density as a buffer pate. Incorporating Allee effects into management and bio- against unexpected loss (the precautionary principle; Lauck economic models is thus critical to long-term sustainability et al. 1998). If catastrophes are infrequent, however, this ap- (Landeetal.1994,1995),especiallyforexploitedpopulations proach would producesuboptimalcatch mostyears. Instead, divided across multiple populations (Stephens and Suther- managers could use a network of marine protected areas land 1999; Frank and Brickman 2000) or subject to high envi- (MPAs), including fully no-take reserves, to maintain high- ronmental variability (Fryxell et al. 2010). density regions while fishing at MSY levels elsewhere (De As anthropogenic warming intensifies, many ecosystems Leo and Micheli 2015). After a catastrophe, larval dispersal areexperiencinggradualyetinexorableenvironmentalchange. from the successfully breeding MPAs can bolster recruit- In marine ecosystems, increased temperature, acidification, ment in neighboring low-density regions where recruitment deoxygenation, and disrupted hydrodynamic and productiv- failure may occur, protecting against the Allee effect (Quinn ity patterns are shifting species ranges and altering their life et al. 1993; Shepherd and Brown 1993; Allison et al. 2003). histories(Waltheretal.2002;ParmesanandYohe2003;Perry Although prior work has considered the effectiveness of re- et al. 2005; Harley et al. 2006; Fabry et al. 2008; Cheung et al. serves as a buffer against environmental uncertainty (Man- 2009; Hoegh-Guldberg and Bruno 2010; Doney et al. 2012). gel 2000; Halpern et al. 2006), catastrophes (Allison et al. In addition to long-term trends, climate change can also in- 2003; McGilliard et al. 2011), or Allee effects (Quinn et al. crease the likelihood of extreme environmental events and 1993) separately, here we explore, for the first time, how ef- sudden shifts (Jentsch et al. 2007; Hegerl et al. 2011). Many fective a range of management strategies are in maintaining marine species are threatenedbyprolongedtemperaturespikes aharvested speciesthat experiences high environmentalvar- (e.g., Dayton and Tegner 1984; Garrabou et al. 2009; Wern- iability and catastrophic events and whose dynamics at low berg et al. 2013), including major impacts of the 2015–2016 density are characterized by the Allee effect. El Niño on coral reefs (Normile 2016). Higher temperatures In this study, we investigated whether the use of spatial and altered upwelling patterns contribute to a greater inci- management via a system of no-take zones can protect a sed- dence of hypoxia and associated mass mortality (Diaz 2001; entary species with Allee-driven recruitment failure from ex- Grantham et al. 2004; Chan et al. 2008; Vaquer-Sunyer and tinction during catastrophic mortality events and, possibly, Duarte 2008). These “catastrophes,” which typically involve speed postcatastrophe recovery of abundance and catch com- high proportional mortality applied broadly across the popu- pared with nonspatial management. We used the green aba- lation, canbe difficulttopredictandintegrate intosustainable lone (Haliotis fulgens) fishery at Isla Natividad, in Baja Cal- management (Wagner et al. 2007; Game et al. 2008; Gephart ifornia Sur, Mexico (Rossetto et al. 2015), as our reference et al. 2017). Species with low mobility and reduced reproduc- case.Abalone(Haliotisspp.)arebroadcastspawnersandhave tive success at low density—that is, those experiencing Allee been shown to have low recruitment success when their abun- effects—are particularly vulnerable to mass mortality events. danceislow(BabcockandKeesing1999;Rogers-Bennettetal. Sessile individuals, such as coral and oysters, or those un- 2004; Blaud 2013; Catton and Rogers-Bennett 2013). In the able to quickly move to avoid a local environmental extreme, US state of California, they have been heavily impacted by suchasmanysedentarybenthicinvertebratesandfish,cannot fishing for decades, with many populations at less than 1% of relocate to avoid stressful high-temperature or low-oxygen their unfished abundance (Rogers-Bennett et al. 2002). There conditions. is ample evidence that abalone populations experience sud- One strategy for maintaining a fishery managed at MSY den mass mortality events. For some species—for example, after an unexpected mass mortality event is to close it as long the black abalone (H. cracherodii)—outbreaks of withering as necessary to allow the population to recover. However, if syndrome have caused rapid and extreme decline in south- population density at MSY was already close to the Allee ern California (Lafferty and Kuris 1993). Mexican fisheries threshold, a catastrophic event may push it below the min- have been strictly managed over the past decades, after pop- imum density for recovery, and the population may collapse ulations were reduced by excessive fishing and extreme and fail to recover despite a complete cessation of fishing El Niño–Southern Oscillation events (Shepherd et al. 1998;

Morales-Bojórquez et al. 2008). More recently, prolonged likelihood of fishery collapse and calculated mean catch and hypoxic events have caused mass abalone die-offs of 50%– proportion recovered after 20 years (the typical length of the 75% at Isla Natividad (Micheli et al. 2012). However, the vol- abalone concession granted to fishing cooperatives in Mex- untary no-take marine reserves established and enforced by ico; McCay et al. 2014). the fishing cooperative of Isla Natividad maintained higher postcatastrophe density (due to the removal of all fishing- associated mortality in the reserves) and significantly larger Material and Methods abalone sizes compared with the fished regions, with corre- Model Description spondingly higher recruitment and larval spillover across the reserve boundaries, indicating that reserves can support the WeusedaspatiallyexplicitIPM(EllnerandRees2006)tosim- resilience of impacted populations (Micheli et al. 2012). ulate recruitment, survival, and growth of green abalone (Ha- Previous models of abalone populations from Isla Nativ- liotis fulgens) within a continuous size structure. All model idad and southern California have concluded that recovery parameters and equations are given in appendix A. We used times after extreme depletion can be long (decades) but that a probabilistic nonnegative growth function (Bardos 2005) networks of small reserves decrease the risk of extinction and to model annual abalone growth (fig. 1A). This growth model buffer populations against management errors, such as set- was developed to accommodate the strongly variable growth ting quotas that are too high (Catton and Rogers-Bennett dynamics of abalone as seen in field data from Troynikov et al. 2013; Rossetto et al. 2015). However, despite robust evidence (1998) and to model population dynamics using length alone of Allee effects in abalone recruitment, previous work on the rather than size-at-age conversion. Abalone survival in natu- effects of MPAs on abalone recovery did not account for the ral environments increases linearly with body mass, which risk of recruitment failure following mass mortality events. can be estimated from length (fig. 1B; Rossetto et al. 2012). McGilliard et al. (2011) assessed recovery with MPAs after Similarly, egg production for mature adults increases expo- mild catastrophes but did not include any form of negative nentially with length (fig. 1C; Tutschulte 1976). density dependence (i.e., decrease in recruitment at low den- Following Button’s (2008) empirical study, we modeled sities). Rossetto et al. (2015) simulated fishery recovery from the Allee effect by assuming that breeding success is an in- overexploitation without considering depensation or regional creasing and saturating function of spawner density that lev- mass mortality. Here, we address these critical biological and els off to 1 at high density and tends to 0 at low density (fig. 1D). environmental processes—Allee effects and environmental The threshold density below which recruitment begins to fail shocks—and their possible influences on future persistence determines the strength of the Allee effect and affects the of abalone populations and fisheries and, by extension, ma- chance of population recovery after a mass mortality event. rine species with similar life-history characteristics, via a mod- Although recent studies have emphasized the importance of eling framework that is generally applicable to broadcast- Allee effects for conservation (Courchamp et al. 1999; Ste- spawning benthic invertebrates. phens and Sutherland 1999), it is still unclear how broadly ap- Our model builds on the spatially explicit stage-structured plicable they are to marine species. Myers et al. (1995) found model developed by Rossetto et al. (2013, 2015) to study ma- evidence of recruitment failure due to low population den- rine reserve impact on abalone population persistence and sity in a few fisheries, but the signal can be hard to discern fishery production. Because abalone fecundity and survival, (LiermannandHilborn1997,2001)andrecentmeta-analyses asinmanymarineinvertebrates,aresensitivetosmallchanges found little evidence across a wide range of taxa (Hilborn et al. in size (Rossetto et al. 2012, 2013), we extended the original 2014). However, Tegner (1993) found that isolated abalone modeling framework based on arbitrary size classes and de- populations were unable to recover following a fishery clo- veloped a novel integral projection model (IPM; Ellner and sureuntilrecruitmentwasaugmentedbylarvaldispersalfrom Rees 2006), allowing continuous size structure. Following nearby transplants, suggesting that Allee effects are poten- Catton and Rogers-Bennett (2013), we added an Allee effect tially important to sedentary invertebrates. The assumption producing diminished fertilization success at low adult den- of the existence of an Allee effect in the stock being managed sity. Using this model, we analyzed postcatastrophe (defined is critical to the applicability of our model. Given the harvest here as 150% mortality) recovery under threerealistic constant- assumptions, postcatastrophe recovery is guaranteed if there effort management strategies: no closure, temporary fishery is no threshold below which recruitment begins to fail. In ac- closures, and no closure with portions of the coastline desig- cordance with Button (2008), we set the threshold density be- nated as no-take reserves. All of these strategies are used to low which breeding success begins to drop to ∼0.2 abalone/m2 manage coastal fisheries in Baja California (McCay et al. and, to account for the uncertainty in the estimation of this 2014) and around the world. We explored how catastrophe threshold, we tested sensitivity to the strength of the Allee ef- severity and frequency, Allee strength, and carrying capacity fect, including its absence, in appendix C (apps. B, C are avail- affect fishery outcomes. For each scenario, we determined the able online).

Figure 1: Population dynamic elements of the model. A, Growth by size. The horizontal and vertical axes indicate starting length and amount of growth, respectively. Growth is distributed across a range, with brightness indicating the relative proportion of the size class growing a speciﬁc amount. B, Survival based on length. Horizontal and vertical axes indicate length and survival proportion. C, Fecundity based on length. Horizontal and vertical axes indicate length and total egg production for mature individuals. D, Allee effect. Shown is the relative breeding success based on the density of mature adults. The dashed line indicates the density associated with roughly 80% breeding success, the default value for the baseline model.

We modeled the coastline of Isla Natividad as a circular set annually, representing a constant level of effort. For the non- of 150 blocks measuring 100 m (alongshore) by 500 m (off- spatial management strategies, we set hNC to 2/3 of the fishing fi shore; distance based on shable habitat as determined by pressure producing MSY (FMSY), as determined by prior sim- Rossetto et al. [2015]) and containing subpopulations con- ulation without catastrophes (app. B). This is the standard nected via stochastic larval dispersal (fig. 2A). We assumed precautionary reference point typically used in fisheries man- that larvae dispersed in a Gaussian fashion with a mean dis- agement(Jenningsetal.2001)tooffseterrorsinparameteres- persal distance that, based on field observations (Micheli et al. timationanduncertaintiesinstockassessmentandpopulation 2012), varies stochastically from year to year according to a dynamics. It is generally considered a good compromise be- gamma distribution (modal distance of 300 m from field data; tween maximizing sustainable yields and minimizing risk of fig. 2B). We further assumed a closed system, with offshore collapse. The harvest rate in the fishable ground under the larval input or loss assumed to be compensatory with no net MPA strategy was set so that the spatial mean of the harvest- effect on local recruitment and annual fluctuations in relative ing rate along the entire coastline (including the protected settler survival rate due to year-to-year environmental vari- areas where h p 0) was equal to that under the no-closure fi p = 2 ability ( g. 2C; Szuwalski et al. 2015). We assumed density- strategy, that is, hMPA hNC (1 fpc), where fpc is the over- p = dependent settlement and set the per-patch carrying capacity all fraction of protected coastline and hNC 2 3FMSY. to produce an unfished density of ∼0.2 ind./m2, based on the work of McShane (1991) and Daume et al. (2004) and con- Analysis of Management Strategies sistent with field observations (Rogers-Bennett et al. 2004; and Catastrophe Scenarios Micheli et al. 2008). We assumed homogeneous habitat both within and between patches. Conventional management without reserves was simulated

We modeled catch as a constant proportion h of as constant harvest pressure hNC with either no interruption commercial-size abalone harvested from each ﬁshable patch (the no-closure or NC strategy) or a moratorium on harvest

Figure 2: Spatial and stochastic elements of the model. A, Circular coastline with Gaussian dispersal. The coastline is divided into 150 blocks 100 m in width and extending 500 m from the shoreline, each with an independent abalone population. Blocks are linked through Gaussian dispersal of larvae, with blocks at each end considered to be neighbors. B, Distribution of mean dispersal distances. Mean dispersal distance is drawn stochastically for each time step from a gamma distribution, and the Gaussian is scaled accordingly. C, Recruitment strength. Relative fi recruitment strength for each time step is drawn from a lognormal distribution with mean rm and standard deviation rsd and modi es settler survival as a multiplier. after the catastrophe until stock had recovered to 150% of tion; Worm et al. 2006; Costello et al. 2008). We repeated the precatastrophe density (the dynamic-closure or DC strat- simulation 1,000 times and calculated two metrics: the pro- egy). We set the reopening threshold for the DC strategy as portionrecovered(i.e.,theproportionofsimulationsinwhich the point at which catch is maximized without substantially catch recovered above the 10% threshold) and the 20-year decreasing the likelihood of recovery in the default scenario catch (i.e., the total present-day value of catch over the 20 years (app. C; fig. C2B; figs. B1, C1–C3 are available online). The following the catastrophe, discounted 5% annually). NC and DC strategies had no area set aside as reserves, while We ran a sensitivity analysis of model outcomes with re- 20% of the fishing ground was protected under the MPA spect to the severity of the catastrophic event (ranging from strategy with six 500-m reserves (the optimal size derived moderate [i.e., 50%] to extreme [i.e., 90%] mortality) and from Rossetto et al. [2015] and our own sensitivity analysis; compared the baseline scenario (one moderate catastrophic see app. C and fig. C3B). We conducted a sensitivity analysis event causing 75% mortality) with multiple-catastrophe sce- of model outcomes with respect to (i) the fraction of fishing narios (two moderate catastrophes 15, 10, or 5 years apart and ground under protection (ranging from 10% to 80%), (ii) the three moderate catastrophes 5 years apart). As there is con- size of each MPA (1, 2, 5, 10, and 15 km), and (iii) dispersal siderable uncertainty about abalone carrying capacity—that distance (from 25% to 200% of the default dispersal distance, is,theunfishedpopulationdensity—wealsoanalyzedtheper- with a 25% increment for each scenario). Harvest rate in the formance of management scenarios under alternative as- fished patches under the MPA strategy was kept constant sumptions of the precatastrophe population density rang- (i.e., no fishing closure) for the entire simulation time. For ing from low (∼0.06 ind./m2 for the NC strategy at 60% of each management strategy, we ran the model with the re- baseline, unfished carrying capacity) to high (∼0.25 ind./m2 spective fishing pressure (hNC for NC and DC and hMPA for at 200%). Because we assumed that precatastrophe manage- theMPAstrategy)untilanequilibrium wasreachedandthen ment was sustainable and error-free, we adjusted harvest pres- applied a global catastrophic event causing 75% mortality to sure to match the FMSY for each density (app. B). allageclasses(the“severe”catastrophescenario).Wethenran The results from additional scenarios and sensitivity anal- the model for an additional 150 years and assessed whether yses are given in appendix C. All simulations were run using the population recovered or collapsed (remained below 10% the programming language R (ver. 3.2.1; R Development Core of precatastrophe maximum catch at the end of the simula- Team 2012).

Results cover depended on a combination of factors, including (i) local replenishment (i.e., postcatastrophe density), (ii) whether For the baseline scenario, the combination of Allee effect and fishing activities are halted after a catastrophic event or not the catastrophe increased the likelihood of collapse of a fish- (NC vs. DC strategies), and/or (iii) larval input from high- ery that would be otherwise sustainable in the absence of density regions (NC vs. MPA strategies; fig. 3). extreme environmental conditions (fig. 3A). Because the de- Our simulation showed that the presence of MPAs was cline of breeding success is nonlinear (fig. 1D), fishery col- abletoavoidfisherycollapseafteracatastropheincaseswhere lapse occurred as a threshold effect from the intersection of uninterrupted harvest with fishing effort at precatastrophe lev- three factors: precatastrophe equilibrium density, strength els would prevent recovery (figs. 3, 4). Under the no-closure of the Allee effect, and severity of the catastrophe. The Allee (NC) management strategy, the likelihoodof recoverydropped effect intensified further when population density was below quickly with increasing catastrophe strength, with only 56% ∼0.2 ind./m2, the carrying capacity in the baseline scenario. of simulation runs recovering after a severe catastrophe and Catastrophe severity (figs. 4, 5) and precatastrophe density 0.1% after an extreme one (fig. 4A, diamonds). Implementing (fig.6)determinedhowfarthepopulationdroppedbelowthe a dynamic postcatastrophe fishery closure (the DC strategy) Alleethreshold.Theabilityofaharvestedsubpopulationtore- decreased the risk of collapse to 1.7% for the baseline scenario

Figure 3: Time series for baseline model with three management strategies. The first and second columns correspond to the constant effort model without and with a dynamic postcatastrophe harvest moratorium, and the third column shows results for the 20% marine protected area (MPA) network. Horizontal axes indicate time, with a severe catastrophe (75% mortality) occurring at t p 150. Vertical axes indicate abalone adult density for the first two rows and cumulative catch in metric tons for the third row. Solid lines show mean density within fished regions for recovering populations, dashed lines show mean density within reserves, and dotted lines show mean density for collapsing fisheries. A–C, Full management-specific time series of stock density. Percentage indicates the fraction of 100 simulation runs that collapsed. D–F, Close-up of the 50-year postcatastrophe recovery period. G–I, Cumulative postcatastrophe catch in the 50-year postcatastrophe recovery period.

Figure 4: A, Catch and population recovery proportion for each management strategy under varying catastrophe severity. The vertical axis indicates the proportion recovered, that is, the proportion of simulation runs that recovered following the catastrophe. The horizontal axis indicates the 20-year catch, that is, the mean cumulative catch over the 20-year postcatastrophe period. Catch was discounted 5% annually, and only noncollapsing simulation runs were included. The contours link the three management strategy outcomes for each catastrophe scenario. Catastrophe severity ranges from moderate (50% mortality) in the upper right to extreme (90% mortality) in the lower left, increasing by 5% increments. The baseline scenario (75% mortality) is indicated by a dashed contour line. B, Mean length of ﬁshery closure for the dynamic-closure model. The horizontal axis indicates catastrophe severity, and the vertical axis shows mean length of closure. Error bars show 1 SD. MPA p marine protected area.

(fig. 4A, dashed line) and to 39% for extreme catastrophes pacity (∼0.4 ind./m2), there is little likelihood of collapse fol- (fig. 4A, circles), but at the cost of greatly reducing catch due lowing a severe catastrophe regardless of management strat- to closure times in excess of 10 years (fig. 4B). However, es- egy (fig. 6A, upper right). As carrying capacity decreases, the tablishment of an MPA network (the MPA strategy) dropped probability of recovery decreases rapidly for the NC strategy the risk of collapse to 0%–0.1% for moderate to severe ca- and gradually for the DC and MPA strategies but remains tastrophes and to substantially less than that for the NC strat- higher for the DC strategy for more severe catastrophes egy for higher severity catastrophes (fig. 4A, triangles). Catch (fig. 6A). As for the other scenarios, catch was substantially for the MPA strategy was ∼73%–89% that of the NC strategy, lower for the DC strategy because of long mean closure times depending on the scenario (fig. 4). (10–30 years; fig. 6B). When multiple moderate catastrophes (50% mortality) These results suggest that MPA networks are more effec- occurred during the simulation time, the DC strategy pro- tive than constant MSY-based fisheries management in mit- tected the fishery from collapse only marginally better than igating the risk of fishery collapse following a mass mortal- the NC strategy in most scenarios, and the MPA strategy ity event. When compared with the use of dynamic fisheries was superior to both nonspatial strategies, reducing the pro- closures, moreover, the MPA strategy provided recovery like- portion collapsed to almost zero for all dual-catastrophe sce- lihoods almost as high for moderate to severe catastrophes narios (fig. 5A). The 20-year catch was similar between the while maintaining high catch due to no fishery closure. After three strategies but was lower for the DC strategy as catastro- a severe catastrophe (fig. 4A, dashed line scenario), for ex- phe frequency increased because multiple catastrophes ne- ample, the MPA strategy reduced the likelihood of collapse cessitated multiple fishery closures (fig. 5B), which reduced to near zero, similar to the DC strategy, but catch was 142% the harvest. higher than that of the DC strategy. For more extreme ca- For a given catastrophe severity, the degree to which post- tastrophes, the MPA strategy had substantially lower recovery catastrophe population density is below the Allee threshold likelihood, but 20-year catch for the DC strategy was near zero depends on precatastrophe density. With high carrying ca- due to long closures (fig. 4A,4B). The higher precatastrophe

Figure 5: A, Catch and population recovery proportion for each management strategy under varying catastrophe number and frequency. The axes are as described in figure 4A. The scenarios are as follows: one moderate (50% mortality) catastrophe (solid line), two moderate catastrophes 15 years apart (dashed-dotted line), two moderate catastrophes 10 years apart (long-dashed line), two moderate catastrophes 5 years apart (short-dashed line), and three moderate catastrophes 5 years apart (dotted line). B, Mean length of fishery closure for the dynamic- closure model. Same as for figure 4B, except that the horizontal axis shows the five catastrophe categories described above. MPA p marine protected area. population density within the reserve translated to higher post- Discussion catastrophe density and allowed larval dispersal from the reserves to rescue the fished regions negatively impacted by In recent decades, climate change and the increased frequency the Allee effect. In the case of multiple moderate catastrophes, of extreme events such as droughts, floods, heat waves, and— this dynamic made the MPA strategy clearly superior to the specific to aquatic environments—prolonged hypoxia have DC strategy (fig. 5A). added additional burden to the many anthropogenic stress- As shown above, increased severity of catastrophe and ors that threaten the persistence of natural populations of lower precatastrophe population density both increased the conservation and commercial interest. Mass mortality events likelihood of collapse and slowed down recovery. In appen- can reduce a population to unexpectedly low densities, ex- dix C, we explore the sensitivity of model results to other fac- ceeding the variability factored into standard “ecological sta- tors. Both an Allee effect stronger than the default empirically bility” management models (Roughgarden and Smith 1996). estimatedfollowingButton(2008;i.e.,highersensitivity ofag- The effects of low population density extend beyond recruit- gregation size to density; fig. C1) and greater mean larval dis- ment failure, with implications for behavior, predator inter- persal distance (fig. C3C) increased the risk of catastrophic action, environmental modification, patch choice, and more collapse of the fishery. Greater larval dispersal sped up recov- (Stephens and Sutherland 1999). ery in the fished areas due to higher larval spillover, but the Risk of local extinction is greatly exacerbated when rel- lower larval retention resulted in lower equilibrium density evant fitness/demographic parameters, such as fertilization within the MPAs and thus a smaller buffer against catastro- rate, fecundity, and/or survival, decrease in sparse, low- phes.Similarly,decreasingthepercentageofthecoastinMPAs density populations. For wild populations that experience or decreasing the size of individual MPAs also increased the Allee effects, it is thus crucial to understand how to avoid chance of collapse (fig. C3A,C3B). For the nonspatial strate- the “extinction vortex” and improve resilience to mass mor- gies, a decrease in proportion of FMSY decreased both catch and tality events by acting on the spatial and temporal distri- the chance of collapse (fig. C2A), with a similar trend for the bution of those anthropogenic stressors that can be directly reopening threshold for the DC strategy (fig. C2B). managed. While the Allee effect is a central concept in ecol-

Figure 6: A, Catch and population recovery likelihood for each management strategy under varying carrying capacity. The axes are as described in figure 4A. Carrying capacity ranges from high (0.4 ind./m2, or 200% of baseline carrying capacity K) in the upper right to low (0.1 ind./m2, or 50% of K) in the lower left, decreasing by increments of 10% of K. The baseline scenario (0.2 ind./m2) is indicated by a dashed contour line. Note that because harvest proportion h is set dynamically for each scenario, proportional change in precatastrophe population density does not exactly match proportional change in K. B, Mean length of fishery closure for the dynamic-closure model. Same as for figure 4B, except that the horizontal axis indicates relative precatastrophe density. MPA p marine protected area. ogyandconservationbiology,mostquantitativestudieshave at low density are characterized by an Allee effect. Networks focused on viability assessment for spatially homogenous of protected areas can effectively increase resilience if their populations (e.g., Ortigosa et al. 2000) or are in the context size and spatial layout are able to maintain a breeding pop- of meta-population frameworks (Amarasekare 1998; Kuus- ulation sufficient to rebuild the reproductive potential de- saari et al. 1998; Brassil 2001). In this work, we investigated spite the presence of Allee effects (Allison et al. 2003; Wag- the interaction among (i) large-scale mass mortality events, ner et al. 2007; Game et al. 2008). Our results are consistent (ii) fine-scale distribution of anthropogenic disturbance in with the general finding that management using protected the form of fishing mortality, and (iii) recruitment dispersal areas provides a buffer against uncertainty, which in fisher- on a spatially explicit coastal habitat for populations with ies reduces catch variability and smooths the effects of re- Allee effects and explored how alternative configurations cruitmentstochasticity(Laucketal.1998;Mangel2000;Rod- of spatial and temporal reduction in anthropogenic distur- well and Roberts 2004; Halpern et al. 2006; Pitchford et al. bance can increase the resilience of populations subject to 2007; West et al. 2009; Barnett and Baskett 2015). Species increased frequency and intensity of extreme events. We de- with Allee effects are particularly sensitive to negative sec- veloped the analysis with specific reference to marine popu- ondary effects from anthropogenic disturbance, such as fish- lations of broadcast spawners, for which Allee effects have ing mortality (Petersen and Levitan 2001; Fryxell et al. 2010), been clearly documented and whose persistence is relevant withincreaseduncertaintyofrecovery(Kuparinenetal.2014), for their ecological and conservation value as well as for the and our results confirm that spatial management can miti- ecosystem services they deliver in terms of seafood produc- gate this vulnerability. Although occasional cessation of har- tion in coastal fisheries. vest can be used in a nonspatial strategy to avoid dropping Our model predicts that a network of protected areas that below an Allee threshold (e.g., Kar and Matsuda 2007), such reduce or possibly eliminate anthropogenic disturbance can a management strategy might not be sufficient in the case of minimize the risk of population collapse caused by large- strong and unpredictable external sources of mortality and scale extreme climatic events for species whose dynamics increasing frequency of extreme and catastrophic events.

McGilliard et al. (2011) predicted that for sustainably abalone, lobster, and other marine invertebrates and algae managed fishery stocks, as with our model, MPAs in com- beginning in the 1930s (McCay et al. 2014). At Isla Nativi- bination with fishing mortality reduction (i.e., catch limita- dad and other locations in this region, MPAs were volun- tion) would greatly decrease the likelihood of catastrophe- tarily established and enforced by the fishing cooperatives, induced population collapse compared with catch regulation which conduct surveillance of their fishing grounds and of alone. For harvested populations already in decline, however, the reserves. Thus, poaching and noncompliance with no- strict catch limitations alone were superior, according to take regulations are minimal (Micheli et al. 2012). In other McGilliard et al. (2011), to MPA establishment without fish- regions, local closures can face significant opposition, and ing reduction unless the model included substantial errors in noncompliance and poaching can negate the potential ben- catch assessment. There are four key differences between our efits of closures (Edgar et al. 2014). Displaced fishing effort modeling analysis and that of McGilliard et al. (2011) that may exert negative impacts on populations and habitat out- might explain this discrepancy. First, their model had a sin- side reserves or leave the industry rather than relocating, in- gle MPA (in contrast to an optimal network of MPAs), thus creasing the catch “penalty” of the MPA strategy (Hilborn minimizing the potential positive effects of larval spillover. et al. 2004; Abbott and Haynie 2012). For abalone, spillover Second, the catastrophes considered by McGilliard et al. from the MPA occurs via larval dispersal, but for a fishery (2011) were significantly less severe than those simulated with with mobile, harvestable adults, reallocated effort along the our model. Third, their model did not include size structure, MPA boundary (e.g., Murawski et al. 2005; Stelzenmüller eliminating the recruitment benefits gained from protecting et al. 2008) can potentially reduce overall catch (Kellner et al. large oldspawners withinMPAs. Fourthandmostimportant, 2007) and may hinder postcatastrophe recovery. their population model had no negative density-dependent Another potential challenge is an increase in harvest as a effects in recruitment, so it did not account for the risk of re- species becomes rare due to increasing prices (the anthropo- cruitment failure when population density in fished areas genic Allee effect; Courchamp et al. 2006; Hall et al. 2008). In dropped below the Allee threshold. the case of green abalone at Isla Natividad, prices are set by The impact on ecosystem services, especially seafood pro- the global market and are not affected by local abundance, but duction, of conservation strategies aimed at increasing the for some species (such as, in the past, white abalone in Cal- resilience of population to extreme climatic events should ifornia;Davisetal.1998)theincreaseinillegalharvestcandis- also be accounted for, as it might also have a positive effect rupt management efforts. Aquaculture is a potential outlet on the short-term social acceptability of alternative conserva- for displaced fishing effort, especially in response to rising tion schemes. Our analysis shows that spatial management global seafood demand, and has been successful for some ab- through a network of protected areas may come at the cost alone species (Searcy-Bernal et al. 2010). However, aquacul- of a decrease in total catch withMPAs depending on scenario, ture operations are also at risk from extreme events that can both pre- and postcatastrophe, compensated by a dramatic impactaquacultureinfrastructureandspeciesthroughstorms, dropinthechanceoffishery collapse. The value of this trade- harmful algal blooms, acidification, and hypoxia. The possi- off depends on the expected frequency and severity of catas- ble role of aquaculture in contributing to seafood production trophes and how likely the population is to experience repro- and income in small-scale fisheries in the face of environ- ductive failure following a sudden drop in abundance. Booth mental variability and extremes remains to be addressed. et al. (2014) showed a 15-year decreasing trend in dissolved Disease outbreaks, an increasing source of mass mortal- oxygen in southern California, for example, which may lead ity in marine systems (Harvell et al. 2004), represent a par- to more frequent extreme hypoxia events. For slow-growing ticular challenge for marine reserves (McCallum et al. 2005; species, an economically viable 5–10-year fishery closure is Wootton et al. 2012). If disease transmission increases with likely insufficient to guarantee recovery from a severe decline density, the impact of outbreaks may be intensified within below the Allee threshold and therefore extended protection MPAs, diminishing their effectiveness (McCallum et al. 2005). in MPAs is more effective, whereas short-term closures may However, our model focused on low densities near the Allee be preferable for fast-growing species (e.g., Cudney-Bueno threshold for which we do not expect disease dynamics to be et al. 2009). Even when catastrophes are expected to be rare strong, particularly during the immediate postcatastrophe and moderate, the uninterrupted annual income that the period. Additionally, some diseases have a strong environ- MPA management approach allows may be preferable for mental trigger (e.g., abalone withering syndrome; Ben-Horin fishers to a lengthy fishery closure. While an individual fisher et al. 2013) and may produce mass mortality events with lit- may be able to tolerate a fishing closure as long as 5 years, a tle density-dependent transmission. Last, as McCallum et al. fishing moratorium lasting 10 or 15 years out of a 20-year (2005) demonstrate, the presence of pathogens can decrease concession would likely be financially unsustainable. reserve performance only down to that of conventional man- Coastal fisheries of Baja California are managed by fish- agement, not below. Consequently, we expect our results to ing cooperatives that were granted exclusive access rights to apply broadly even in the presence of disease outbreaks.

As with all simulations, our model makes a number of sim- should expand the spatial and economic aspects of the model plifying assumptions to reduce computational complexity to include a more detailed tactical simulation of small-scale and produce a more general outcome. On the basis of Button spatial heterogeneity in habitat type and quality and variabil- (2008), we assume a simple nonlinear shape to the Allee ef- ity in reserve spacing (Kaplan and Botsford 2005); realistic fect, with a rapid decrease in breeding success starting at dispersal patterns accounting for oceanographic conditions roughly 0.2 ind./m2. While this is consistent with prior exper- and, when applicable, larval behavior; and the incorporation imental work and field observations, density is a proxy only of a more complex model for the distribution of fishing effort. for aggregation size and calculations based on observed den- For example, dynamic closures may be more effective when sity during field surveys may overestimate the Allee effect local population abundances and dispersal patterns vary (Lit- (Lundquist and Botsford 2011). Abalone may aggregate in tle et al. 2010). In addition, while adult abalone are gener- larger groups during spawning, allowing successful fertiliza- ally sedentary, other benthic invertebrates may be capable of tion even at low densities (Micheli et al. 2008, 2012; but see moving over distances similar to the patch size modeled Coates et al. 2013). A more linear decline in breeding success here, and adult movement outside MPAs is known to par- would also diminish the power of the Allee effect, as is sug- tially reduce the efficacy of protection (Moffitt et al. 2009; gested by theoretical models of aggregation and sperm dis- De Leo and Micheli 2015). persal (Lundquist and Botsford 2004), which would poten- Despite these caveats, we believe that our analysis is ro- tially eliminate the recovery advantages of the MPA strategy bust and suggests that the interaction of low-frequency, high- (app. C; fig. C1A). Our model does not include demographic risk events and inverse density dependence can unexpectedly stochasticity, but we would not expect any significant effect raise the risk of collapse for an otherwise sustainably man- until densities were much lower than those seen here (the de- aged species. This model, the first to analyze the benefits of fault Allee threshold of 0.2 ind./m2 is equivalent to 10,000 in- protected areas for managing catastrophic die-off in density- dividuals per block). The Gompertz growth function we use sensitive stock, improves our understanding of the potential in this model assumes nonnegative growth of abalone shell, disruptiveeffectoflow-frequency,high-riskeventswhenman- eventhoughreductionofabaloneconditionhasbeenobserved aging under uncertainty and provides a quantitative frame- in some cases (Button and Rogers-Bennett 2011) and did not worktoaccountfortheeffectsofsuddenmassmortalityevents provide the best fit for abalone growth data in some prior when balancing persistence and human use in the design of studies (Rogers-Bennett et al. 2007). long-term management plans. Allee effects are expected to Our model used a simple homogenous spatial structure be common in nature (Kramer et al. 2009), and it is crucial to that ignores potentially important factors, such as spatial het- understand how to improve the resilience of managed species erogeneities in local productivity, fishing pressure, and larval if they are to survive in the face of steadily increasing tem- dispersal. Catastrophes such as extreme hypoxia are unlikely peratures (Coumou et al. 2013), acidifying oceans (Hoegh- to be global in scale (affecting optimal MPA placement; Wag- Guldberg and Bruno 2010), and large-scale extreme events ner et al. 2007) or, additionally, to produce size-independent occurring with greater and greater frequency (Coumou and mortality. Clark et al. (2013) found that, for clams, large ma- Rahmstorf 2012). ture adults were the most vulnerable to hypoxia, which, if true of abalone, would potentially decrease the postcatastrophe Acknowledgments fecundity of the MPAs and thus their ability to buffer against collapse. Finally, genetic data from Isla Natividad suggest that, We thank the Walton Family Foundation, the US National while there is measurable gene flow from external sources, Science Foundation (NSF) Dynamics of Coupled Natural and there is insufficient input of larvae to create a “rescue effect” Human Systems (CNH) program (award DEB-1212124), and when local populations are low (Munguía-Vega et al. 2015). the US NSF Ocean Acidification (OA) program (agreement Consequently, we believe that the year-to-year variability in OCE-1416934). We thank members and staff of the fishing recruitment success, as implemented in our model, provides cooperative Buzos y Pescadores and of Comunidad y Biodi- sufficient stochasticity to implicitly account for moderate res- versidad for their support and advice as well as Greg Dwyer cue effects from larval supplement from exogenous sources and two anonymous referees for their constructive criticism as well as fluctuating environmental conditions. We expect on early versions of the manuscript. the recovery benefits of the MPA strategy to be greatest for a fishery with infrequent pulses of larvae or older individuals APPENDIX A from external sources. Finally, we have assumed a homogenous habitat, symmet- Model Parameters and Equations ric larval dispersal, and simplified bioeconomic conditions. Future work addressing persistence of exploited marine pop- For each patch z of the discretized coastline, following Ell- ulations in the face of environmental variability and extremes ner and Rees (2006), the population density (ind./m2)at

This content downloaded from 171.066.209.130 on February 05, 2019 15:37:11 PM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). 000 The American Naturalist time t 1 1 for a given length l is described by the following Survival equation: The instantaneous mortality rate m(l) for abalone in natural ð environments is related linearly to body mass w(l) (Rossetto p j 1 0 j 0 0 0 ð Þ nz,t11(l) G(l L0)Rz,t (S(z, l , l)G(l l ))nz,t (l )dl , A1 et al. 2012), which can be estimated from length (Shepherd 1998): where n (l) is the number of individuals of size l at time t z,t ln m(l) p v 1 a ln w(l), ðA7Þ in patch z; Rz,t is the annual recruits at time t in patch z; L0 0 F p ⋅ bw ð Þ is the initial length of recruits; G(l l ) is the growth function, w(l) aw l , A8 that is, the probability to grow from size l0 to size l in 1 year; 0 and S(z, l , l) is the survival function, accounting for both size- where v, a, aw, and bw are scaling parameters. dependent natural mortality and fishing mortality. Note that We calculated annual survival for an individual in patch z initial survival for new recruits is already incorporated into by integrating instantaneous survival from starting length l0 to ending length l1 and assuming that all harvest occurs at the the Rz,t value. Growth, survival, fecundity, dispersal, and catch fi end of the year: functions are de ned below. 8 ð > l1 > 2 2m(l) 1 ∈ <(1 h) e dl if l1 LminH, z Zf , Growth S(z, l , l ) p ð l0 0 1 > l1 :> 2m(l) We used a probabilistic nonnegative Gompertz growth func- e dl otherwise, l tion to model annual green abalone growth (Gompertz 1825; 0 ðA9Þ Bardos 2005). This function creates a distribution of possible growth increments Dl for any specific starting length l and where h is the constant annual harvest proportion based on avoids negative growth by allowing maximum length L∞ to the assumption of constant effort, LminH is the minimum har- fi “ ” vary dynamically with l. The mean and variance of L∞ are de- vest size, and Zf is the set of shed patches (see Catch be- termined by Ln and jL, respectively, with associated scaling low). parameters b and g. Thus, the probability of an abalone of length l growing by the length increment Dl is Fecundity r l 2 r 1 2l(L∞2l) The number of eggs produced in each patch z at time t is G(Dljl) p (L∞ 2 l) e G(r) calculated as follows from eggs per unit of mass ew and the = G2 , ðA2Þ 1 Dl 1 l 1 (e 1) total mature female biomass (assuming a 1∶1 sex ratio) in # fi 1 2 e2G l patch z (Tutschulte 1976; Rossetto et al. 2013), modi ed by the Allee effect Alleez,t: where G istheGompertzgrowthparameter,G() is the gamma ð n (l) function, and E p Allee ⋅ e p (l)w(l) z,t dl: ðA10Þ z,t z,t w mature 2 no2G 2 1=(12e ) 2e G ð Þ fi L∞ p (l 1 Dl)l , A3 The proportion of reproductive individuals for a speci c length l is = 1 b = 3 p 1 Ln 1 ( (l Ln)) pmature(l) , ðA11Þ l p , ðA4Þ 1 1 exp(2(l 2 L )=a ) = 1 = 3 2 mat mat (jL (1 (g(l Ln)) )) where amat is a scaling parameter and Lmat is the length at which half of individuals are mature (Rossetto et al. 2013). = 1 b = 3 2 Ln (1 ( (l Ln)) ) r p : ðA5Þ The Allee effect in patch z at time t, Alleez,t, is determined = 1 = 3 jL (1 (g(l Ln)) ) by mean aggregation size Aggz,t: p : ð Þ Alleez,t Pmixed(Aggz,t) A12 The five parameters of the Gompertz growth function (G, Ln, j b g L, , and ) were estimated by Rossetto et al. (2015) by min- Aggz,t is calculated using the total density of mature individ- imizing the following negative log-likelihood function using uals Mz,t, observed abalone growth data: ð p ð Þ X Mz,t pmature(l)nz,t (l)dl, A13 p j : log(L) log(p(Dly ly)) ðA6Þ y to estimate mean aggregation size (Button 2008),

p ⋅ 1 fi Aggz,t aagg Mz,t bagg, ðA14Þ and a lognormal distribution ( g. 2C) that represents relative annual fluctuations in settler survival rate due to year-to-year and is used to determine the probability of mixed gender ag- environmental variability (Szuwalski et al. 2015). gregations: Following Micheli et al. (2008) and Rossetto et al. (2013), 2 p 2 : Aggz,t 1: ð Þ we modeled recruitment Rz,t as a Ricker function (Ricker Pmixed(Aggz,t ) 1 0 5 A15 1954) of the form The aggregation regression parameters aagg and bagg were derived from Button (2008) by setting the 80% breeding suc- S R p j S exp 2 z,t , ðA18Þ cess threshold for the Allee effect to 0.2 mature adults per z,t S z,t K square meter. This value is similar to that seen in prior work (0.15–0.2 [Shepherd and Brown 1993; Shepherd and Part- with density dependence occurring only at the settlement ington 1995] and 0.3 [Babcock and Keesing 1999]) and is stage, carrying capacity K, and r(t) in equation (A17) ac- consistent with recruitment failure seen in the field (failure counting for year-to-year environmental variability. at 0.003 vs. success at 0.85; Rogers-Bennett et al. 2004). Catch Dispersal, Settlement, and Recruitment Catch is calculated in metric tons as Larval dispersal was assumed to be Gaussian with a mean ð X Lmax dispersal distance d(t) that varies stochastically from year to p 26 Ct 10 A hxw(l)nz,t (l)dl, ðA19Þ LminH year according to a gamma distribution with shape ds and Zf rate d . The fraction of larvae r dispersing k patches away r fi from the source patch, with k p51,52, ::: was thus com- where A is the area of each patch and Zf is the set of shable puted as follows: patches (i.e., those that are not set aside as no-take zones). ð Harvest proportion hx is the proportion of commercial size 100(k1(1=2)) 1 fi p pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2= 2 : ð Þ abalone that is harvested from each shable patch in year t r(k) exp( x 2jd(t))dx A16 2 = 2 for management scenario x: 100(k (1 2)) 2pjd(t) 8 The number of settlers in patch z at time t was calculated > 2 p < FMSY if x NC, DC, summing the contribution of all patches j as follows: 3 X h p ðA20Þ x > h S p r(t)j E r(jj 2 zj), : NC p z,t E j,t ðA17Þ 2 if x MPA, j (1 fpc) where j is the set of patches, jE represents the survival from where FMSY is the harvest rate associated with the MSY and eggs to settlers, and r(t) is a random variable with mean p 1 fpc is the fraction of protected coastline.

Table A1: Model parameter values Parameter Symbol Value Unit Source Population dynamics:

Length at recruitment L0 1mm

Length for 50% maturity Lmat 135.99 mm a

Minimum harvest length LminH 155 mm a

Annual harvest proportion hx Variable b # 25 2bw Weight scaling value aw 2.24 10 gmm c

Weight exponent bw 3.36 c No-shell weight proportion .4 a Gompertz growth parameter G .5635 d

Gompertz maximum length mean Ln 150.39 mm d 2 Gompertz maximum length variation jL 55.95 d Gompertz mean scaling b 1.478 d Gompertz variation scaling g 1.719 d Mortality scaling a 2.317 e Mortality intercept v .635 e

Maturity scaling value amat 30.2 mm a

Table A1 (Continued) Parameter Symbol Value Unit Source

21 Fecundity ew 3,772 eggs g f

Slope for aggregation estimate aagg 11.6 g

Intercept for aggregation estimate bagg 1g

Survival of eggs jE .005704 h

Survival of recruits jS .01 a Carrying capacity for recruits K 1.29 # 107 individuals i Spatial/stochastic: Length of coastline 15,000 m Length of block 100 m Width of block 500 m Area of each block A 5 # 104 m2

Mean dispersal distance gamma shape ds 3j

Mean dispersal distance gamma rate dr .006 j

Recruitment lognormal mean rm 0k

Recruitment lognormal standard deviation rsd .7 k a From Rossetto et al. (2015). b fi Harvest proportion was scenario speci c and equal to 2/3 of FMSY for the nonspatial management strategy. Total harvest for the spatial p : management strategy was set to be equivalent, adjusted for fraction of protected coastline. For the default scenario, hNC 0 06 and p : hMPA 0 075. c From Shepherd et al. (1998). d Parameters from Bardos (2005) model estimated by fitting observed growth data, as described in Rossetto et al. (2015). e Mortality parameters are for Haliotis fulgens from Rossetto et al. (2012). Similar to non-size-dependent values seen in other abalone literature (M p 0:38 [Shepherd 1990]; M p 0:77 [Button and Rogers-Bennett 2011]). f From Tutschulte (1976). g The aggregation regression is from Button (2008) with slight alterations. We changed aagg from 11.3 to 11.6, a value within the given 95% 2 p p uncertainty range, to set 80% breeding success to 0.2 ind./m . We set the intercept bagg 1 instead of 1.959 so that aggregation size 1 when density approaches zero. h The original egg survival value from Rossetto et al. (2013) was 3.09 # 1023. We adjusted this survival value by 1.846 to remove the implicit Allee effect estimated from the observed densities of 0.015 ind./m2. i The original estimated value of K from McShane (1991) and Daume et al. (2004) was 107. We adjusted this slightly to produce a mean unfished density of ∼0.2 ind./m2 in each block. j The distribution parameters were determined by Rossetto et al. (2015), based off an observed modal dispersal distance of ∼300 m (Micheli et al. 2012). k Following the observations of Shepherd (1990), we set these values to produce an ∼15# ratio between highest and lowest recruitment years after trimming outliers.

Literature Cited Bardos, D. C. 2005. Probabilistic Gompertz model of irreversible growth. Bulletin of Mathematical Biology 67:529–545. Abbott, J. K., and A. C. Haynie. 2012. What are we protecting? fisher Barnett, L. A. K., and M. L. Baskett. 2015. Marine reserves can enhance behavior and the unintended consequences of spatial closures as a ecological resilience. Ecology Letters 18:1301–1310. fishery management tool. Ecological Applications 22:762–777. Ben-Horin, T., H. S. Lenihan, and K. D. Lafferty. 2013. Variable inter- Allee, W. C. 1932. Animal life and social growth. Williams & Wilkins tidal temperature explains why disease endangers black abalone. in cooperation with the Century of Progress Exposition, Baltimore. Ecology 94:161–168. Allison, G. W., S. D. Gaines, J. Lubchenco, and H. P. Possingham. Berec, L., E. Angulo, and F. Courchamp. 2007. Multiple Allee effects 2003. Ensuring persistence of marine reserves: catastrophes require and population management. Trends in Ecology and Evolution adopting an insurance factor. Ecological Applications 13:S8–S24. 22:185–191. Amarasekare, P. 1998. Allee effects in metapopulation dynamics. Amer- Blaud, B. M. 2013. Spatial and temporal patterns of fertilization in ican Naturalist 152:298–302. black abalone (Haliotis cracherodii Leach, 1814): analysis of surro- Babcock, R. C., and J. Keesing. 1999. Fertilization biology of the aba- gate gamete spawning experiments with application towards pop- lone Haliotis laevigata:laboratoryandfield studies. Canadian Jour- ulations on San Nicolas Island, California. MS thesis. University of nal of Fisheries and Aquatic Sciences 56:1668–1678. Washington, Seattle. Babcock, R. C., S. Kelly, N. T. Shears, J. W. Walker, and T. J. Willis. Boettiger, C., and A. Hastings. 2013. No early warning signals for sto- 1999. Changes in community structure in temperate marine reserves. chastic transitions: insights from large deviation theory. Proceedings Marine Ecology Progress Series 189:125–134. of the Royal Society B 280:20131372.

Booth, J. A. T., C. B. Woodson, M. Sutula, F. Micheli, S. B. Weisberg, Diaz, R. J. 2001. Overview of hypoxia around the world. Journal of S. J. Bograd, A. Steele, J. Schoen, and L. B. Crowder. 2014. Patterns Environmental Quality 30:275–281. and potential drivers of declining oxygen content along the south- Dirzo,R.,H.S.Young,M.Galetti,G.Ceballos,N.J.B.Isaac,andB. ern California coast. Limnology and Oceanography 59:1127–1138. Collen.2014.DefaunationintheAnthropocene.Science345:401–406. Brassil, C. E. 2001. Mean time to extinction of a metapopulation with Dobson, A. P., and J. Poole. 1998. Conspecific aggregation and con- an Allee effect. Ecological Modelling 143:9–16. servation biology. Pages 193–208 in T. Caro, ed. Behavioral ecology Button, C. A. 2008. The influence of density-dependent aggregation and conservation biology. Oxford University Press, Oxford. characteristics on the population biology of benthic broadcast- Doney, S. C., M. Ruckelshaus, J. Emmett Duffy, J. P. Barry, F. Chan, spawning gastropods: pink abalone (Haliotis corrugata), red abalone C. A. English, H. M. Galindo, et al. 2012. Climate change impacts (Haliotis rufescens), and wavy turban snails (Megastraea undosa). on marine ecosystems. Annual Review of Marine Science 4:11–37. PhD diss. University of California, San Diego. Dunham, J., M. Peacock, C. R. Tracy, J. Nielsen, and G. Vinyard. Button, C. A., and L. Rogers-Bennett. 2011. Vital rates of pink abalone 1999. Assessing extinction risk: integrating genetic information. Haliotis corrugata estimated from mark-recapture data to inform Conservation Ecology 3:2. recovery. Marine Ecology Progress Series 431:151–161. Edgar, G. J., R. D. Stuart-Smith, T. J. Willis, S. Kininmonth, S. C. Catton, C. A., and L. Rogers-Bennett. 2013. Assessing the recovery of Baker, S. Banks, N. S. Barrett, et al. 2014. Global conservation out- pink abalone (Haliotis corrugata) by incorporating aggregation into comes depend on marine protected areas with five key features. a matrix model. Journal of Shellfish Research 32:181–187. Nature 506:216–220. Chan, F., J. A. Barth, J. Lubchenco, A. Kirincich, H. Weeks, W. T. Pe- Ellner, S. P., and M. Rees. 2006. Integral projection models for species terson, and B. A. Menge. 2008. Emergence of anoxia in the Cali- with complex demography. American Naturalist 167:410–428. fornia current large marine ecosystem. Science 319:920. Fabry, V. J., B. A. Seibel, R. A. Feely, and J. C. Orr. 2008. Impacts of Cheung, W. W. L., V. W. Y. Lam, J. L. Sarmiento, K. Kearney, R. ocean acidification on marine fauna and ecosystem processes. Watson, and D. Pauly. 2009. Projecting global marine biodiversity ICES Journal of Marine Science 65:414–432. impacts under climate change scenarios. Fish and Fisheries 10:235– Fagan, W. F., and E. E. Holmes. 2005. Quantifying the extinction 251. vortex. Ecology Letters 9:51–60. Clark, M. S., G. Husmann, M. A. S. Thorne, G. Burns, M. Truebano, Frank, K. T., and D. Brickman. 2000. Allee effects and compensatory L. S. Peck, D. Abele, and E. E. Philipp. 2013. Hypoxia impacts large population dynamics within a stock complex. Canadian Journal of adults first: consequences in a warming world. Global Change Biol- Fisheries and Aquatic Sciences 57:513–517. ogy 19:2251–2263. Fryxell, J. M., C. Packer, K. McCann, E. J. Solberg, and B.-E. Sæther. Coates, J. H., K. A. Hovel, J. L. Butler, A. Peter Klimley, and S. G. 2010. Resource management cycles and the sustainability of har- Morgan. 2013. Movement and home range of pink abalone Haliotis vested wildlife populations. Science 328:903–906. corrugata: implications for restoration and population recovery. Game, E. T., M. E. Watts, S. Wooldridge, and H. P. Possingham. Marine Ecology Progress Series 486:189–201. 2008. Planning for persistence in marine reserves: a question of cat- Costello, C., S. D. Gaines, and J. Lynham. 2008. Can catch shares pre- astrophic importance. Ecological Applications 18:670–680. vent fisheries collapse? Science 321:1678–1681. Garrabou, J., R. Coma, N. Bensoussan, M. Bally, P. Chevaldonne, M. Coumou, D., and S. Rahmstorf. 2012. A decade of weather extremes. Cigliano, D. Diaz, et al. 2009. Mass mortality in Northwestern Med- Nature Climate Change 2:491–496. iterranean rocky benthic communities: effects of the 2003 heat wave. Coumou, D., A. Robinson, and S. Rahmstorf. 2013. Global increase Global Change Biology 15:1090–1103. in record-breaking monthly-mean temperatures. Climatic Change Gascoigne, J. 2004. Allee effects in marine systems. Marine Ecology 118:771–782. Progress Series 269:49–59. Courchamp, F., E. Angulo, P. Rivalan, R. J. Hall, L. Signoret, L. Bull, Gephart, J. A., L. Deutsch, M. L. Pace, M. Troell, and D. A. Seekell. and Y. Meinard. 2006. Rarity value and species extinction: the an- 2017. Shocks to fish production: identification, trends, and conse- thropogenic Allee effect. PLoS Biology 4:e415. quences. Global Environmental Change 42:24–32. Courchamp, F., T. Clutton-Brock, and B. Grenfell. 1999. Inverse den- Gilpin, M. E., and M. E. Soulé. 1986. Minimum viable populations: sity dependence and the Allee effect. Trends in Ecology and Evolu- processes of extinction. Pages 19–34 in M. E. Soulé, ed. Conservation tion 14:405–410. biology: the science of scarcity and diversity. Sinauer, Sunderland, Cudney-Bueno, R., M. F. Lavín, S. G. Marinone, P. T. Raimondi, and MA. W. W. Shaw. 2009. Rapid effects of marine reserves via larval dis- Gompertz, B. 1825. On the nature of the function expressive of the persal. PLoS ONE 4:e4140. law of human mortality, and on a new mode of determining the Daume, S., S. Huchette, S. Ryan, and R. W. Day. 2004. Nursery culture value of life contingencies. Philosophical Transactions of the Royal of Haliotis rubra: the effect of cultured algae and larval density on Society B 115:513–583. settlement and juvenile production. Aquaculture 236:221–239. Grantham, B. A., F. Chan, K. J. Nielsen, D. S. Fox, J. A. Barth, A. Davis, G., P. L. Haaker, and D. Richards. 1998. The perilous condition Huyer, J. Lubchenco, and B. A. Menge. 2004. Upwelling-driven of white abalone Haliotis sorenseni, Bartsch, 1940. Journal of Shell- nearshore hypoxia signals ecosystem and oceanographic changes fish Research 17:871–875. in the northeast Pacific. Nature 429:749–754. Dayton, P. K., and M. J. Tegner. 1984. Catastrophic storms, El Niño, Hackney, E. E., and J. B. McGraw. 2008. Experimental demonstra- and patch stability in a southern California kelp community. Science tion of an Allee effect in American ginseng. Conservation Biology 224:283–285. 15:129–136. De Leo, G. A., and F. Micheli. 2015. The good, the bad and the ugly Hall, R. J., E. J. Milner-Gulland, and F. Courchamp. 2008. Endanger- of marine reserves for fishery yields. Philosophical Transactions of ing the endangered: the effects of perceived rarity on species ex- the Royal Society B 370:20140276. ploitation. Conservation Letters 1:75–81.

Halpern, B. S., H. M. Regan, H. P. Possingham, and M. A. McCarthy. ———. 1995. Optimal harvesting of fluctuating populations with a 2006. Accounting for uncertainty in marine reserve design. Ecology risk of extinction. American Naturalist 145:728–745. Letters 9:2–11. Lauck, T., C. W. Clark, M. Mangel, and R. M. Gordon. 1998. Im- Harley, C. D. G., A. R. Hughes, K. M. Hultgren, B. G. Miner, C. J. B. plementing the precautionary principle in fisheries management Sorte, C. S. Thornber, L. F. Rodriguez, L. Tomanek, and S. L. Wil- through marine reserves. Ecological Applications 8:S72–S78. liams. 2006. The impacts of climate change in coastal marine sys- Levin, S. A., and J. Lubchenco. 2008. Resilience, robustness, and ma- tems. Ecology Letters 9:228–241. rine ecosystem-based management. AIBS Bulletin 58:27–32. Harvell, C. D., R. Aronson, N. Baron, J. Connell, A. P. Dobson, S. Levitan, D. R., M. A. Sewell, and F.-S. Chia. 1992. How distribution and Ellner, L. Gerber, et al. 2004. The rising tide of ocean diseases: un- abundance influence fertilization success in the sea urchin Strongylo- solved problems and research priorities. Frontiers in Ecology and centotus franciscanus. Ecology 73:248–254. the Environment 2:375–382. Liermann, M., and R. Hilborn. 1997. Depensation in fish stocks: a Hegerl, G. C., H. Hanlon, and C. Beierkuhnlein. 2011. Climate sci- hierarchic Bayesian meta-analysis. Canadian Journal of Fisheries ence: elusive extremes. Nature Geoscience 4:142–143. and Aquatic Sciences 54:1976–1984. Hilborn, R., D. J. Hively, O. P. Jensen, and T. A. Branch. 2014. The ———. 2001. Depensation: evidence, models and implications. Fish dynamics of fish populations at low abundance and prospects for and Fisheries 2:33–58. rebuilding and recovery. ICES Journal of Marine Science 71:2141– Little, L. R., R. Q. Grafton, T. Kompas, and A. D. M. Smith. 2010. Clo- 2151. sure strategies as a tool for fisheries management in metapopula- Hilborn, R., K. Stokes, J.-J. Maguire, T. Smith, L. W. Botsford, M. tions subjected to catastrophic events. Fisheries Management and Mangel, J. Orensanz, et al. 2004. When can marine reserves improve Ecology 17:346–355. fisheries management? Ocean and Coastal Management 47:197–205. Lundquist, C. J., and L. W. Botsford. 2004. Model projections of the Hobday, A. J., M. J. Tegner, and P. L. Haaker. 2000. Over-exploitation fishery implications of the Allee effect in broadcast spawners. Eco- of a broadcast spawning marine invertebrate: decline of the white logical Applications 14:929–941. abalone. Reviews in Fish Biology and Fisheries 10:493–514. ———. 2011. Estimating larval production of a broadcast spawner: Hoegh-Guldberg, O., and J. F. Bruno. 2010. The impact of climate the influence of density, aggregation, and the fertilization Allee ef- change on the world’s marine ecosystems. Science 328:1523–1528. fect. Canadian Journal of Fisheries and Aquatic Sciences 68:30–42. Hutchings, J. A., and J. D. Reynolds. 2004. Marine fish population Mangel, M. 2000. Irreducible uncertainties, sustainable fisheries and collapses: consequences for recovery and extinction risk. BioScience marine reserves. Evolutionary Ecology Research 2:547–557. 54:297–309. McCallum, H. I., L. Gerber, and A. Jani. 2005. Does infectious disease Jennings, S., M. J. Kaiser, and J. D. Reynolds. 2001. Marine fisheries influence the efficacy of marine protected areas? a theoretical frame- ecology. Blackwell Science, Oxford. work. Journal of Applied Ecology 42:688–698. Jentsch, A., J. Kreyling, and C. Beierkuhnlein. 2007. A new generation McCauley, D. J., M. L. Pinsky, S. R. Palumbi, J. A. Estes, F. H. Joyce, and of climate-change experiments: events, not trends. Frontiers in Ecol- R. R. Warner. 2015. Marine defaunation: animal loss in the global ogy and the Environment 5:365–374. ocean. Science 347:247–254. Kaplan, D. M., and L. W. Botsford. 2005. Effects of variability in spac- McCay, B. J., F. Micheli, G. Ponce-Díaz, G. Murray, G. Shester, S. ing of coastal marine reserves on fisheries yield and sustainability. Ramirez-Sanchez, and W. Weisman. 2014. Cooperatives, conces- Canadian Journal of Fisheries and Aquatic Sciences 62:905–912. sions, and co-management on the Pacific coast of Mexico. Marine Kar, T. K., and H. Matsuda. 2007. Sustainable management of a fish- Policy 44:49–59. ery with a strong Allee effect. Trends in Applied Sciences Research McGilliard, C. R., A. E. Punt, and R. Hilborn. 2011. Spatial structure 2:271–283. induced by marine reserves shapes population responses to catas- Keith, D. M., and J. A. Hutchings. 2012. Population dynamics of marine trophes in mathematical models. Ecological Applications 21:1399– fishes at low abundance. Canadian Journal of Fisheries and Aquatic 1409. Sciences 69:1150–1163. McShane, P. E. 1991. Density-dependent mortality of recruits of the Kellner, J. B., I. Tetreault, S. D. Gaines, and R. M. Nisbet. 2007. Fishing abalone Haliotis rubra (Mollusca: Gastropoda). Marine Biology the line near marine reserves in single and multispecies fisheries. 110:385–389. Ecological Applications 17:1039–1054. Micheli, F., A. Saenz-Arroyo, A. Greenley, L. Vazquez, J. A. Espinoza Kramer, A. M., B. Dennis, A. M. Liebhold, and J. M. Drake. 2009. Montes, M. Rossetto, and G. A. De Leo. 2012. Evidence that marine The evidence for Allee effects. Population Ecology 51:341–354. reserves enhance resilience to climatic impacts. PLoS ONE 7:e40832. Kuparinen, A., D. M. Keith, and J. A. Hutchings. 2014. Allee effect Micheli, F., A. O. Shelton, S. M. Bushinsky, A. L. Chiu, A. J. Haupt, and the uncertainty of population recovery. Conservation Biology K. W. Heiman, C. V. Kappel, et al. 2008. Persistence of depleted 28:790–798. abalones in marine reserves of central California. Biological Con- Kuussaari, M., I. Saccheri, M. Camara, and I. Hanski. 1998. Allee ef- servation 141:1078–1090. fect and population dynamics in the Glanville fritillary butterfly. Moffitt, E. A., L. W. Botsford, D. M. Kaplan, and M. R. O’Farrell. Oikos 82:384–392. 2009. Marine reserve networks for species that move within a home Lafferty, K. D., and A. M. Kuris. 1993. Mass mortality of abalone range. Ecological Applications 19:1835–1847. Haliotis cracherodii on the California Channel Islands: tests of ep- Morales-Bojórquez, E., M. O. Muciño-Díaz, and J. A. Vélez-Barajas. idemiological hypotheses. Marine Ecology Progress Series 96:239– 2008. Analysis of the decline of the abalone fishery (Haliotis fulgens 248. and H. corrugata) along the westcentral coast of the Baja California Lande, R., S. Engen, and B.-E. Sæther. 1994. Optimal harvesting, eco- peninsula, Mexico. Journal of Shellfish Research 27:865–870. nomic discounting and extinction risk in fluctuating populations. Mullon, C., P. Freon, and P. Cury. 2005. The dynamics of collapse in Nature 372:88–90. world fisheries. Fish and Fisheries 6:111–120.

Munguía-Vega, A., A. Sáenz-Arroyo, A. P. Greenley, J. A. Espinoza- Rossetto, M., G. A. De Leo, A. Greenley, L. Vazquez, A. Saenz-Arroyo, Montes, S. R. Palumbi, M. Rossetto, and F. Micheli. 2015. Marine J. A. Espinoza Montes, and F. Micheli. 2013. Reproductive potential reserves help preserve genetic diversity after impacts derived from can predict recruitment rates in abalone. Journal of Shellfish Re- climate variability: lessons from the pink abalone in Baja California. search 32:161–169. Global Ecology and Conservation 4:264–276. Rossetto, M., F. Micheli, A. Saenz-Arroyo, J. Espinoza Montes, and Murawski, S. A., S. E. Wigley, M. J. Fogarty, P. J. Rago, and D. G. G. A. De Leo. 2015. No-take marine reserves can enhance popula- Mountain. 2005. Effort distribution and catch patterns adjacent to tion persistence and support the fishery of abalone. Canadian Jour- temperate MPAs. ICES Journal of Marine Science 62:1150–1167. nal of Fisheries and Aquatic Sciences 72:1503–1517. Myers, R. A., N. J. Barrowman, J. A. Hutchings, and A. A. Rosenberg. Roughgarden, J., and F. Smith. 1996. Why fisheries collapse and what 1995. Population dynamics of exploited fish stocks at low popula- to do about it. Proceedings of the National Academy of Sciences of tion levels. Science 269:1106–1108. the USA 93:5078–5083. Myers, R. A., J. A. Hutchings, and N. J. Barrowman. 1997. Why do fish Sadovy, Y., and M. Domeier. 2005. Are aggregation-fisheries sus- stocks collapse? the example of cod in Atlantic Canada. Ecological tainable? reef fish fisheries as a case study. Coral Reefs 24:254–262. Applications 7:91–106. Saha, B., A. R. Bhowmick, J. Chattopadhyay, and S. Bhattacharya. 2013. Normile, D. 2016. El Niño’s warmth devastating reefs worldwide. On the evidence of an Allee effect in herring populations and conse- Science 352:15–16. quences for population survival: a model-based study. Ecological Ortigosa, G. R., G. A. De Leo, and M. Gatto. 2000. VVF: integrating Modelling 250:72–80. modelling and GIS in a software tool for habitat suitability assess- Searcy-Bernal, R., M. R. Ramade-Villanueva, and B. Altamira. 2010. ment. Environmental Modelling and Software 15:1–12. Current status of abalone fisheries and culture in Mexico. Journal Parmesan, C., and G. Yohe. 2003. A globally coherent fingerprint of of Shellfish Research 29:573–576. climate change impacts across natural systems. Nature 421:37–42. Shepherd, S. A. 1990. Studies on southern Australian abalone (genus Perry, A. L., P. J. Low, J. R. Ellis, and J. D. Reynolds. 2005. Climate Haliotis). XII. Long-term recruitment and mortality dynamics of change and distribution shifts in marine fishes. Science 308:1912– an unfished population. Australian Journal of Marine and Fresh- 1915. water Research 41:475–492. Petersen, C. W., and D. R. Levitan. 2001. The Allee effect: a barrier to ———. 1998. Studies on southern Australian abalone (genus Ha- recovery by exploited species. Pages 281–300 in J. D. Reynolds, liotis). XIX. Long-term juvenile mortality dynamics. Journal of G. M. Mace, K. H. Redford, and J. G. Robinson, eds. Conservation Shellfish Research 17:813–825. of exploited species. Cambridge University Press, Cambridge. Shepherd, S. A., and L. D. Brown. 1993. What is an abalone stock: im- Pitchford, J. W., E. A. Codling, and D. Psarra. 2007. Uncertainty and plications for the role of refugia in conservation. Canadian Journal sustainability in fisheries and the benefit of marine protected areas. of Fisheries and Aquatic Sciences 50:2001–2009. Ecological Modelling 207:286–292. Shepherd, S. A., and D. Partington. 1995. Studies on southern Austra- Quinn, J. F., S. R. Wing, and L. W. Botsford. 1993. Harvest refugia in lian abalone (genus Haliotis). XVI. Recruitment, habitat and stock marine invertebrate fisheries: models and applications to the Red Sea relations. Marine and Freshwater Research 46:669–680. urchin, Strongylocentrotus franciscanus. American Zoologist 33:537– Shepherd, S. A., J. R. Turrubiates-Morales, and K. Hall. 1998. Decline 550. of the abalone fishery at La Natividad, Mexico: overfishing or cli- Radovich, J. 1982. The collapse of the California sardine fishery. Cali- mate change? Journal of Shellfish Research 17:839–846. fornia Cooperative Oceanic Fisheries Investigations Reports 23:56– Stelzenmüller, V., F. Maynou, G. Bernard, G. Cadiou, M. Camilleri, 78. R. Crec’hriou, G. Criquet, et al. 2008. Spatial assessment of fish- R Development Core Team. 2012. R: a language and environment ing effort around European marine reserves: implications for suc- for statistical computing. R Foundation for Statistical Computing, cessful fisheries management. Marine Pollution Bulletin 56:2018– Vienna. 2026. Ricker, W. E. 1954. Stock and recruitment. Journal of the Fisheries Stephens, P. A., and W. J. Sutherland. 1999. Consequences of the Al- Board of Canada 11:559–623. lee effect for behaviour, ecology and conservation. Trends in Ecol- Rodwell, L. D., and C. M. Roberts. 2004. Fishing and the impact of ma- ogy and Evolution 14:401–405. rine reserves in a variable environment. Canadian Journal of Fish- Stoner, A. W., M. H. Davis, and C. J. Booker. 2012. Negative conse- eries and Aquatic Sciences 61:2053–2068. quences of Allee effect are compounded by fishing pressure: com- Rogers-Bennett, L., B. L. Allen, and G. E. Davis. 2004. Measuring ab- parison of queen conch reproduction in fishing grounds and a ma- alone (Haliotis spp.) recruitment in California to examine recruit- rine protected area. Bulletin of Marine Science 88:89–104. ment overfishing and recovery criteria. Journal of Shellfish Research Szuwalski, C. S., K. A. Vert-Pre, A. E. Punt, T. A. Branch, and R. 23:1201–1207. Hilborn. 2015. Examining common assumptions about recruitment: Rogers-Bennett, L., P. L. Haaker, T. O. Huff, and P. K. Dayton. 2002. a meta-analysis of recruitment dynamics for worldwide marine fish- Estimating baseline abundances of abalone in California for resto- eries. Fish and Fisheries 16:633–648. ration. Reports of California Cooperative Oceanic Fisheries Investi- Tegner, M. J. 1993. Southern California abalones: can stocks be rebuilt gations 43:97–111. using marine harvest refugia? Canadian Journal of Fisheries and Rogers-Bennett, L., D. W. Rogers, and S. A. Schultz. 2007. Modeling Aquatic Sciences 58:2010–2018. growth and mortality of red abalone (Haliotis rufescens) in north- Troynikov, V. S., R. W. Day, and A. M. Leorke. 1998. Estimation of ern California. Journal of Shellfish Research 26:719–727. seasonal growth parameters using a stochastic Gompertz model Rossetto, M., G. A. De Leo, D. Bevacqua, and F. Micheli. 2012. Allomet- for tagging data. Journal of Shellfish Research 17:833–838. ric scaling of mortality rates with body mass in abalones. Oecologia Tutschulte, T. C. 1976. The comparative ecology of three sympatric 168:989–996. abalones. PhD diss. University of California, San Diego.

Vaquer-Sunyer, R., and C. M. Duarte. 2008. Thresholds of hypoxia West, C. D., C. Dytham, D. Righton, and J. W. Pitchford. 2009. Pre- for marine biodiversity. Proceedings of the National Academy of venting overexploitation of migratory fish stocks: the efficacy of Sciences of the USA 105:15452–15457. marine protected areas in a stochastic environment. ICES Journal Wagner, L. D., J. V Ross, and H. P. Possingham. 2007. Catastrophe of Marine Science: Journal du Conseil 66:1919–1930. management and inter-reserve distance for marine reserve networks. Wootton, E. C., A. P. Woolmer, C. L. Vogan, E. C. Pope, K. M. Ham- Ecological Modelling 201:82–88. ilton, and A. F. Rowley. 2012. Increased disease calls for a cost- Walther, G. R., E. Post, P. Convey, A. Menzel, C. Parmesan, T. J. C. benefits review of marine reserves. PLoS ONE 7:e51615. Beebee, J. M. Fromentin, O. Hoegh-Guldberg, and F. Bairlein. 2002. Worm, B., E. B. Barbier, N. Beaumont, J. E. Duffy, C. Folke, B. S. Ecological responses to recent climate change. Nature 416:389–395. Halpern, J. B. C. Jackson, et al. 2006. Impacts of biodiversity loss Wernberg, T., D. A. Smale, F. Tuya, M. S. Thomsen, T. J. Langlois, on ocean ecosystem services. Science 314:787–790. T. de Bettignies, S. Bennett, and C. S. Rousseaux. 2013. An extreme climatic event alters marine ecosystem structure in a global biodiversity hotspot. Nature Climate Change 3:78–82. Associate Editor: Greg Dwyer Editor: Judith L. Bronstein

“Previous to the year 1763 bluefish were very plenty on the southern coast of Cape Code, but about this year they all disappeared, and none were taken till sixty or seventy years after. For the past thirty years specimens have been taken, but they did not arrive in any noticeable abundance till within the last sixteen years, and are at the present time again vanishing.” Figured: Above, “The Haddock, Morrhua æglefinus.” Below, “The Bluefish, Temnodon saltator.” From “The Habits and Migrations of Some of the Marine Fishes of Massachusetts” by James H. Blake (The American Naturalist, 1870, 4:513–521).

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