Downloaded by guest on September 27, 2021 www.pnas.org/cgi/doi/10.1073/pnas.1705169114 in management option fishery superior a be may reserves case. suggest- by that conditions, management these meets that States ground- ing United Coast the West of the fishery how critical fish show most also the of We using many settings. in by multispecies tool management than a rather as dis- advantage a reserves have tinct reserves marine Thus, alone. using approaches stocks nonspatial weak by traditional of ensured, persistence yields be and fisheries, increased, can be many can for stocks that strong of show We with them multi- approaches. managing managing to nonspatial relative of reserves using merits by the fisheries species about to model been conclusions mathematical has general strategic context heuristic obtain a ecosystem develop an we so in problemmixed, reserves’ fisheries ubiquitous manage marine to for and potential Evidence challenging management. this ecosystem-based solving in in reserves play marine that role might recovery the long weak investigate long- very We a is overfished. of requires once stock thus time bycatch and weak fecundity the is low when has problem severe and lived most particular is a problem This high, stocks. gear Because be making of location. with can costs same the fish the selective and of nonselective, in are reside stocks gears that fishing mixed histories many with life deal of range to facing a how challenge is greatest managers the perhaps fishery effective, environments largely mixed data-rich been in had has species has single world managing the Fr While of by success. reviewed fisheries 2015. 2017; in diverse 29, elected the March Sciences of review of Management for Academy (sent National 2017 the 12, of July members Hastings, by Alan Articles by Inaugural Contributed of series special the of part is contribution This 93106 CA Barbara, Santa California, of University a Hastings Alan problem fisheries bycatch in important an solve reserves Marine ac ftesrn tc hl nuigpritneo h weak maximize the to of wants persistence ensuring manager while fishery stock the strong the that extirpation. of given of catch danger as in is take and weak bycatch We the the as is species, harvested second that is a species that is stock, target there and a activity is economic specifi- there of We focus where step. situation important a an model is cally models detailed than rather gic (8). America the North on target of fisheries coasts of groundfish east weak harvest and all the the west nearly of in include persistence cutbacks Examples ensure severe species. entails to reduce often species to this all is stock; of problem rates this catch with The the and dealing (8). fisheries, for commonplace in more approach challenges becoming traditional pressing are disasters most (7), stock more the or species. weak of y target 50 one for the remains known for well it been optimized has is unsustain- problem to this fishing effects driven Although when disastrous are levels that have low stocks” “weak ably may are species these species, others; one these for across for differ decisions rates catch fisheries optimal targets, sustainable secondary most If other species, bycatch. of target or dynamics one the on impact based simultaneously ecosystem- often management Although more are 6). decisions 2, when (1, warranted situations, are reliance approaches in continued based models the is single-species failure management. on scientific and biggest policy, the science, of Arguably, limitations reflect and mon F eateto niomna cec n oiy nvriyo aiona ai,C 51;and 95616; CA Davis, California, of University Policy, and Science Environmental of Department ie h aueo h rbe,a prahbsdo strate- on based approach an problem, the of nature the Given e 13.Dsiemn ucse 4 ) alrsaecom- are failures the 5), in (4, success successes of many record Despite mixed (1–3). a sea has management isheries a,1 tvnD Gaines D. Steven , | aiepoetdarea protected marine b n hitpe Costello Christopher and , | ekstocks weak | bycatch b 1 8903. page on QnAs See interest. of conflict no declare authors The College. Bowdoin G.E.H., and University; McGill F.G., Reviewers: paper. the wrote and data, lyzed though even 15), (12, dynamics sin- include on not focused did reserves or marine species of gle models manage- Initial increasingly ecosystem-based efforts. are of ment they component important area, an an as in simul- touted species reserves marine many better Since impact or 20). (14, taneously 15) mixed empiri- 13, more although is (12, management, evidence of as cal forms well nonspatial as 19) (12, do management than often that can suggest reserves studies including rel- theoretical still is immature, models Although fisheries atively into (12–18). reserves poten- closures marine of of the integration increasing impacts the focused result, fisheries has the a habitats protection on fished As attention from to benefits borders. benefits of they spillover the reserve larvae tial of beyond microscopic some exported the plankton, are or the con- adults to not of do release movement reserves (9–11). marine the of significantly strain pre- boundaries increase of the since commonly size Moreover, species average and and mortality fished densities fishing viously population reducing damage, By habitat to goals. primarily conservation created were achieve areas marine-protected such torically, achieved reserve. be marine could a sustain- than without approaches higher abundance, single-species stock a by man- higher produces species, and always target yield, reserves able the marine than fisheries stock by later of weak agement matures use the and the If longer-lived in reserves. is lie marine may incorporating solution management that effective general models, provide surprisingly multispecies simple also a using will show, cases, stock. approach we weak some Here, strategic the guidance. in our from yield, cases, benefits those stock economic small In strong high be on unacceptably also focus may involves there we often While reducing this (8). species; requires costs all so of doing rates for catch approach traditional The stock. uhrcnrbtos .. ... n ..dsge eerh efre eerh ana- research, performed research, designed C.C. and S.D.G., A.H., contributions: Author owo orsodnesol eadesd mi:[email protected]. Email: addressed. be should correspondence whom To eet semnadconservation. and simultaneously fishermen that that solution benefits a in plaguing be that may problem suggesting reserves fishery, the marine fishery, groundfish is Coast con- this West effort US that fishing the emphasize using We by alone. than trols reserves be can using yields by long- higher is obtained significantly reproduce, stock to weak slow the but even lived, If or problem. alleviate, this can eliminate, fishing completely show to we closed model, areas strategic establishing “weak that general allow and a to Using ubiquitous species persistence. target most stock” the to of the is take solution of reduce usual dramatically The one fisheries. global is pur- in challenges in species, crippling caught another unintentionally of is suit species one where Bycatch, Significance aiersre r ra fteoencoe ofihn.His- fishing. to closed ocean the of areas are reserves Marine ed ´ rcGihr n ulem .Herrera) E. Guillermo and Guichard eric ´ PNAS b rnSho fEvrnetlSine&Management, & Science Environmental of School Bren | uut2,2017 22, August | o.114 vol. | o 34 no. | 8927–8934

SUSTAINABILITY INAUGURAL ARTICLE SCIENCE the problem has long been recognized (7). Others have also ery. This highly diverse fishery highlights the potential practical considered issues of multiple species and the role of reserves importance of our findings, even though it necessarily simplifies (19, 21, 22), but have not specifically addressed the important the life history details and other aspects of this fishery. question we focus on here. In particular, advances based on simulation approaches (23, 24) have yielded important insights Model and Analysis into particular fisheries. We take a different approach to devel- We start with a simple, single-species model with and without oping principles for multispecies management by using simple, reserves. The dynamics of multiple species in a reserve network heuristic models to examine whether marine reserves could help can then be described by keeping track of the densities of each resolve aspects of the weak-stock fisheries problem. species inside and outside of reserves. In the absence of a reserve, Our scientific understanding of the complex dynamics of mul- the discrete-time population dynamics for species i are given by: tispecies fisheries is still limited (25). Simple models with clearly ni,t+1 = Ei [fi (mi ni,t ) + ai ni,t ] [1] stated assumptions can provide general principles to guide deci- sions and can point to future directions for more detailed stud- where ni,t is the density (biomass per length of coastline, where ies. In the context of management of fisheries through the use the coastline is normalized to a length of one) of species i at of marine-protected areas, one example of such a model was time t, Ei is the escapement, the fraction of the stock that is left developed by Hastings and Botsford (15), who showed con- unharvested, the function fi (·) describes the survival of young ditions under which maximum sustainable yield from effort until they recruit to the adult population, mi is the per capita control would be exactly the same as maximum sustainable fecundity, and ai is the survivorship of adults. So far, this model yield obtained from setting aside a portion of the habitat as a is identical to ref. 15. We denote by c the fraction of the coastline marine reserve. Although that model was stylized, so the specific in a no-take marine reserve network. We will keep track of fish assumptions of the model may never be exactly met in practice, stocks in two locations [inside the reserve (R) and outside the R both the generality of the conclusions and the ease with which reserve (O)], so nit is the density of species i inside the reserve O the dependence of the conclusions on the assumptions can be and ni,t is the density outside the reserve in period t. evaluated were key advantages. In fact, the impact of changing Several specific assumptions should be emphasized so that we assumptions could be deduced in many cases without formal cal- later can discuss implications of relaxing these assumptions. We culations. We build on that model here. do not include explicit space; we are assuming that larvae are We make a number of simplifying and conservative assump- widely and uniformly distributed. We do not include specific tions to get a basic understanding of the problem, recogniz- aspects of age structure. We ignore economic aspects such as the ing that, in any particular fishery, not all of the assumptions cost of harvest as a function of fish density. In what follows, we may be met and that more detailed models will be needed to only focus on steady-state yields from the strong stock and do not develop more detailed management plans. Our arguments build explicitly include issues related to yield from the weak stock. on earlier models for single species (12, 15), but with appro- We focus on two species, with subscripts i = w for the weak priate extensions to deal with a multispecies fishery. In partic- stock and i = s for the “strong” stock. Here, the strong stock is ular, we assume that adults are sufficiently stationary to remain the primary target of the fishery. The weak stock is one that would within the reserve; that larvae are so widely distributed that we be reduced to an unacceptably low level (including extinction) can ignore their spatial arrangement; that issues arising from with continued harvest of the strong stock at a rate that maxi- explicit consideration of age structure can be ignored; and that mizes strong-stock yield in the absence of reserves. We formal- all density dependence occurs at the time of larval settlement. ize this definition below. We assume that these species are bio- The effects of deviations from these assumptions can at first be logically independent, but that harvesting is indiscriminate in the dealt with by verbal arguments, and then, in future work, by sense that the harvest makes the escapement the same for both more detailed models. We further assume that the only inter- species, Ew = Es = E, and, similarly, reserves provide full protec- action between species is that they are subject to the same fish- tion for both species. This symmetry implies that the two policy eries management—the same harvest rate outside reserves and levers available to fishery managers are c (fraction of coastline the same protection afforded by a set of reserves. Other interac- in reserve) and E (fraction of stock outside reserves that is left tions are not specifically considered. As a way to demonstrate the unharvested). We will use an equilibrium analysis, so we focus robustness of our conclusions, we will comment on how relaxing on steady state. For convenience, we use escapement as the fish- these assumptions will affect key model results. ery management instrument, but it is a straightforward matter to We proceed in several ways using our simple model. We derive the commensurate harvest quotas. Obviously, questions first use an analytic approach to demonstrate the potential for about dealing with uncertainties and a fishery that is currently reserves to give rise to higher yield of a strong stock, and higher either overexploited or underexploited would be an important population levels of the weak stock, than would management next step in applying this model to real-world settings. without a reserve. This will indicate the kinds of life histories for Incorporating all of this information, we can immediately write weak and strong stocks where reserves would be advantageous. down a system of equations that describes, in steady state so the We then illustrate these results and extend them to conditions subscript t is not used, the densities of species i in and out of that cannot be investigated analytically for general parameter reserves, as follows: values using a numerical investigation of our model. Our ana- R R O R ni = fi (mi (cni + (1 − c)ni )) + ai ni [2] lytic approach begins with conditions for persistence of the weak stock. However, this approach could include persistence at unac- O h R O O i n = E fi (mi (cn + (1 − c)n )) + ai n [3] ceptably low levels, perhaps implying persistence only in a deter- i i i i ministic model and not in a field situation. We thus complement And steady-state yield is given by: the analytic demonstration of the underlying principle with more Y = (1 − E)(1 − c)f (m cnR + (1 − c)nO ) + a nO [4] detailed numerical approaches, parameterized with values from i i i i i i the West Coast groundfish multispecies system. Instead of focus- We assume that the objective of fishery management is to max- ing on the persistence boundary for the weak stock, we require imize equilibrium yield of the strong stock, but that the weak the weak stock to be above a threshold level. stock must not be driven extinct. Eqs. 2–4 can be analyzed to Even though our approach is a strategic one, we finish by mak- select a policy that achieves this goal; we make use of two impor- ∗ ing an empirical comparison with parameters representative of tant benchmarks. First, define by Es the escapement that max- weak and strong stocks for the US West Coast groundfish fish- imizes the yield described by Eq. 4 when c = 0—that is, it is

8928 | www.pnas.org/cgi/doi/10.1073/pnas.1705169114 Hastings et al. Downloaded by guest on September 27, 2021 Downloaded by guest on September 27, 2021 ec onayfrtewa tc sgvnby given is stock persis- weak the the Consequently, that for zero. condition boundary be tence the matrix by this given of is determinant the the species that a sees for one boundary theory, persistence Perrron–Frobenious from ideas Using essec ftewa tc eursta tlatoeeigen- one least at positive: that is requires Jacobian the stock of The weak value persistent). is the stock weak of the thus, persistence weak (and, the unstable is with 0 equilibrium at the stock which under conditions the maximize derive to set is stock. escapement strong the the of when yield persist sustainable not does stock—namely, it weak will a that This describing juveniles. condition additional settling algebraic an of the provide function recruit make decreasing they until monotone will young a of we is survival capita where per stock, the that weak assumption the of sistence case only. this results in the numerical conditions present highest algebraic of we the complex, As frightfully fraction produce stock. become would strong the the than but from greater yield is or zero, reserves positive), is in is coastline reserves reserves reserves outside of outside combination escapement (escapement a through escapement either is and does stock main- than weak that the yield management case, tains higher that reserve In a reserve. a a produces with without managing and managing that persistence but ensures possible, still never is stock strong this by advantaged the be indicate will will reserves This where approach. persists. histories stock life from of weak yield kinds the where, optimal persis- stock, conditions produces the strong determine that the for then policy and reserve-only condition the stock general stock. under weak strong a the the of determining for tence by profit of maximal begin persistence ensure the We and ensure stock both weak will policy the reserve the exist, (where tions policy reserve-only the the and which con- outside whether under asks escapement first exist analysis no ditions our (with insight, this policy using By reserve) reserve-only reserve). no equivalent a (with achieve policy with escapement could or optimal stock an either single with any yield of management that h bec farsre(so reserve a of absence the if and off, dies stock size reserve any For stock strong the for yield of loss a (so generates stock setting escapement strong (i.e., yield This the maximal produce of would escapement what beyond the increasing requires essarily stock, extinct. strong go the will of stock yield weak maximize the to a effort (without means choose traditional and with reserve) fishery (E the rate manage escapement we if the words, under extinct from goes arising that yield from stock by arising strong yield yield the Ref. stock harvested. to strong is alent the reserve that the showed outside 15 everything if of stock strong absence the in by Eq. stock define strong Second, the reserves. for escapement optimal the atnse al. et Hastings trigwt h yai oe mle yEqs. by implied model dynamic the with Starting per- the for conditions determining by analysis the begin We the from yield single-species-optimal that possible also is It ihu eev,esrn essec fawa tc nec- stock weak a of persistence ensuring reserve, a Without E J Y 4 E w = s when (c 0 = <  Y = ) f Y s ed opritneo h eksok fsc condi- such If stock. weak the of persistence to leads ) ∗ 0 s (0)mc ahmtcly edfieawa tc saspecies a as stock weak a define we Mathematically, . ∗ E Ef .W aea trigpitteosrain(15) observation the point starting a as take We ). a w 2 0 = 0 + cE (0)mc + ta s ti h pia eev iefrthe for size reserve optimal the is it is, —that a w a c E (f fescapement if , − w > 0 (0)m 1 E a w w c (c c w 0 = s ∗ + hntewa tc esss In persists. stock weak the then ), [f − h eev ieta maximizes that size reserve the cf 0 ,ti becomes: this ), (0)m 1) w f 0 0 (0)m (0)m − E (1 f w < 0 w − (0)m (1 E − c w − + ) c 1 (c s w ∗ c ednt this denote we ; hnteweak the then ), ) = + a ] E cf − E s ∗ 3 w 0 s .I other In ). ∗ 1 (0)m and  E sequiv- is > c we 4, w = E [5] [6] s ∗ c ). s ∗ where denoted: be can size reserve The reserve. the stock: weak a for stock, hold weak must a condition of lowing definition our by Thus, to reduces which if when example, for satisfied, f is which exam- For survival. of value low a if has ple, stock strong the when stock. case weak strong the the of to persistence advantage the yield ensuring while a Eqs. fishery, offer stock cases, reserves that two under prove the persist strong to in will Because cient identical stock stock. is weak strong yield the the stock (ii) for management and management (no-reserve) stock; reserve-only traditional strong under the off for die fact, in will, Eqs. If under persist is: to policy stock stock weak strong the reserve-only for a condition sufficient if if and reserve, sary persists; the stock outside weak harvested are the fish all if Even E level. harvest reserves so by reserves, stock only outside weak management escapement of the no policy with if a ask institute and we if policy persist reserve-only will the to turn now We htaentaeal oaayi nlss ie h relative the Given model analyses. our analytic of to aspects amenable many not are are there that bycatch, neg- of of the impacts reducing demonstration for ative clear reserves marine a of advantages provide potential the results analytic the Although possible; be Approach not Numerical general may more stock the strong numerically. the to this for move investigate we yield now full We where stringent. case more are tence becomes reserves by traditional solely under management extinct with survive goes and stock (a harvest weak small the very which be under to dition taken is stock strong the condition persistence the zero, becomes stock is weak rate the for escapement Eq. the From policy. when no-reserve 6, the than yield higher provides policy eoigti hehl eev iefrtewa tc by stock weak gives: the rearranging for size reserve threshold this Denoting w 0 a (0)m 0 = lal,a h dl uvvrhpo h togsokincreases, stock strong the of survivorship adult the as Clearly, the typically is this that shows example numerical simple A when satisfied is stock weak the for condition persistence the If s sgetrta eo h odtosfrwa-tc persis- weak-stock for conditions the zero, than greater is E n n eevsaea h level the at are reserves and 9 w s ∗ ∗ and < E stepplto ee ftesrn tc tteoptimal the at stock strong the of level population the is s03 hc satpclvle(5,adtesria of survival the and (15), value typical a is which 0.3, is w 2.5 0 = (0) 13 f h ekstock weak the (i) that ensured are we then hold, w 1 0 c (0)m s PNAS − ∗ a E = 0 a w 2 E w w < E + w 0 = (0) s ∗ | s ∗ f c c a w < < w 0 s uut2,2017 22, August ∗ − w (0)m c > 0.3 (f = a (1 < w w a 0 f f w (0)m − c w + w 1 < 1 w 0 0 w (0)m + (0)m c − − a E f hni isof o neces- a So, off. dies it then , a w w 1 0 + s f ∗ w a a (0)m w w 1 c 0 ) − w w a (0)m s + ∗ f w w − s w hncerytereserve the clearly then , 1 (m c a f | 1) − E w w 1 s 0 = o.114 vol. n (0)m s a s w ∗ 1 − s n s c w ∗ < s  s ∗ ∗ 0 = f 9 ) w and E 0 w ,te h con- the then 1), and (0)m w .8 otefol- the so (0), | E c o 34 no. 13 and w 0 = > r suffi- are c outside w c 0. | then , w 67 [10] [12] [13] [14] [11] 8929 and [8] [7] [9] <

SUSTAINABILITY INAUGURAL ARTICLE SCIENCE simplicity of the model, it is possible to investigate a range Finally, in Fig. 1C, the weak stock is persistent with maxi- of conditions numerically. We do this both for general values mum strong-stock yield, even with no marine reserve. The per- and for parameters estimated from the West Coast groundfish sistence boundary is to the left of the entire curve of options fishery. that maximize strong-stock yield. Although this case does not To implement this model numerically, we need fecundity require a marine reserve, increases in reserve size up to 40% con- and survivorship parameters (m, a) and a specific function for tinue to grow the weak-stock population with no compromise to recruitment that includes postdispersal density dependence and the strong-stock yield. As the reserve size increases to 40%, the survival, f (·) for both the strong and weak stock. For f (·), we use weak-stock population grows from ∼5% of its unfished popula- the Beverton–Holt functional form: tion size to 23%. αn To help ground the three generic cases illustrated in Fig. 1, f (n) = [15] 1 + n/β we also looked at model predictions using data for a group of weak and strong stocks from the highly diverse Eastern Pacific where α is the initial slope (at zero). Under this specification for groundfish fishery, which has historically been plagued by clo- f (n), we can calculate the unfished equilibrium (i.e., the carrying sures due to overfished weak stocks (Fig. 2). Given the very capacity): large number of stocks in this fishery (>90 species), we focus β  αm  on a few illustrative cases. We show projections for four impor- nunfished = − 1 [16] tant overfished stocks—bocaccio, darkblotched rockfish, Pacific m 1 − a Ocean perch, and yelloweye rockfish. For each case, the com- So the persistence requirement (in an unfished state) is: parative strong stock is Dover sole (Microstomus pacificus), a αm stock that is currently viewed as healthy with large annual land- > 1 [17] ings (26). For the prior examples, we used a persistence curve 1 − a defining characteristics that would lead to a population at 5% of its historical unfished size—perhaps enough to forestall extinc- Numerical Results tion, but a very small population size. In this example, we also Our main results are illustrated by Fig. 1. The figure shows the show the 20 and 40% persistence boundaries for each weak yield of the strong stock and the persistence of the weak stock, stock. The latter is meant to parallel the current US policy of for a range of reserve (c) and escapement (E) policies for three rebuilding weak stocks back to levels closer to where their own classes of weak stock species. The background shading is pro- fishery yields would be maximized. Results are similar across portional to equilibrium strong stock yield, where lighter shad- the four weak-stock species; here, we discuss two key findings. ing indicates higher yield. The solid curve represents the persis- First, all four weak-stock species can be made persistent at the tence boundary for the weak stock (here we assume this occurs 5% level with no compromise in strong-stock yield, but only if at 5% of carrying capacity); left and below the curve the weak marine reserves are used (these reserves would be on the order stock dies off, and right and above the curve it persists. Circles of 10% of the area). Second, to achieve higher levels of weak- indicate escapement policies that maximize strong stock yield for stock abundance (say, 20 or 40% of carrying capacity) will any given reserve size; circle size indicates strong stock yield; and require some unavoidable compromises in strong-stock yield, circle color indicates weak stock abundance. but this compromise is generally less stringent when reserves The three examples of weak-stock species represented in Fig. are used. For example, yelloweye rockfish (Fig. 2D) can achieve 1 pose different challenges. One driver could be the scope 20% of its carrying capacity either with no reserve (but a loss of differences in the life history parameters of the weak vs. of 32% in yield of petrale sole) or with a 21% reserve (forego- strong stock species. In the first case (Fig. 1A), maximizing ing just 9% in yield of petrale sole). The only case we found in strong-stock yield in the absence of a reserve will clearly cause which the no-reserve policy might be preferred is with bocac- the weak stock to die off (the largest no-reserve circle is well cio (which, by these calculations, is not a true weak stock, inside the persistence boundary). Simply increasing escapement because it could sustain a population of ∼5% of carrying capac- without a reserve (moving up the 0% reserve axis) entails an ity even under effort-only maximum sustainable yield manage- unavoidable loss in strong-stock yield, but can eventually guar- ment of the strong stock). Even in that case, the losses are antee weak-stock persistence. Alternatively, moderately sized very small. For example, for bocaccio to achieve 20% persis- reserves (between c = 25 and 40%), with the appropriate choice tence, the no-reserve policy entailed a strong-stock yield cost of escapement outside the reserve, can both ensure persistence of 7%, while the reserve policy entailed a strong-stock yield of the weak stock (circles to the right of the persistence bound- cost of 10%. ary) and produce yields equivalent to what would have been pos- sible under optimal single-species management (circles are the Discussion same size as the left-most circle). While even larger reserves will The problem of weak stocks, and bycatch more generally, is ensure persistence of the weak stock, they also entail a loss in one of the most important challenges facing fisheries manage- yield of the strong stock (as c increases above 40%, circles dimin- ment today (27, 28). Without selective gear or practices that can ish in size). Under these parameter values, any reserve between greatly reduce the catch rates of weak stocks, traditional fish- 25 and 40%, matched with appropriate escapement, can achieve eries management has a limited arsenal to combat the prob- maximum sustainable yield of the strong stock and ensure persis- lem. The most widespread policy approach to this problem has tence of the weak stock. This illustrates our main finding. been to reduce harvest rates of all species to avoid extinction of The second case (Fig. 1B) illustrates a weak stock species that the weak stocks. However, the costs of this approach in yield requires more aggressive actions to achieve persistence. Here, of the strong stock can be substantial. It is intuitive that the the persistence boundary is to the right of all possible combina- problem is most severe when the weak stock is much longer- tions of reserve size and escapement that can maintain maximum lived (high survivorship), late maturing, and has lower fecundity sustainable yield for the strong stock. As a result, all options with than the target stock. However, we have shown that these are persistence of the weak stock necessarily require a yield compro- the precise conditions under which reserves provide the great- mise for the strong stock. The magnitude of the compromise dif- est benefit. A long-lived, slow-reproducing weak stock is also fers, however, between the reserve and escapement-only options. the case where overfishing can have the longest-lasting impact, In this case, the yield with a very large reserve is much larger than since its recovery following management failure may be exceed- the best option with sufficiently low escapement for persistence. ingly slow.

8930 | www.pnas.org/cgi/doi/10.1073/pnas.1705169114 Hastings et al. Downloaded by guest on September 27, 2021 Downloaded by guest on September 27, 2021 atnse al. et Hastings survivorship. adult adult low natural with high species with for species are they for than benefit survivorship a of more are reserves the when determines risk. turn, at in is which, stock species, weak target reserve the optimal depen- or for rates density sizes harvest optimal of the form determine will functional dence the the traditional above), of meets it stated independent from (provided conditions dependence is yield density of conclusion the form functional general the than this higher While with be management less management. always from and yield will longer-lived the species, is reserves target stock the weak than the fecund where limitations stock strong in compromise is any stock without weak 40% the to reserve, up a of without reserve even a and from (B); benefit circle (60%) would yield reserve stock; stock stock large weak weak very strong a the the better either although of much requires maximized, produces (C persistence stock is and yield weak option allow yield 25 the stock reserve stock between line of the reserve strong persistence escapement bold any although the ensuring and the which (75%), and (A); size for persistence persistent of escapement reserve species stock of high right stock weak choice very weak the ensure that hypothetical a and to for different yield or yield and three stock The the are strong calculations. above of Shown increase analytic combinations size. appreciation the will population an in 40% parameter used stock get Only 0 weak to of yield. equilibrium circles level indicates largest maximum the shading the including the with levels, with compared population small be compared other should as for size) obtained (circle be yield would stock results strong similar (c arbitrary; size is 5% reserve of boundary of combinations for capacity) 1. Fig. BC A

ersi nesadn forrslsbgn yntn that noting by begins results our of understanding heuristic A weak with fishery multispecies any for that shown have We E Escapement Outside Reserve (E) 20% 40% 60% 80% 20% 40% 60% 80% 0% 0% togsokyed(akrudclradcrl ie n eksokpritnebudr bl uv,rpeetn %o eksokcarrying weak-stock of 5% representing curve, (bold boundary persistence stock weak and size) circle and color (background yield stock Strong %2%4%60% 40% 20% 0% ). %2%4%60% 40% 20% 0% c n togsokecpmn usd h eev (E reserve the outside escapement strong-stock and ) Viability=5% Reserve SizeReserve (c)

8.Cnesl,ormdlde o sinhge ot ocatch (27, to costs species higher target assign signifi- not the does potentially of model have our catches Conversely, also less-efficient 28). from would costs efforts cant reduce these to used but gear when selective advantages bycatch, more have our could that of approaches seem assumptions other might or the It violated. that be ways would additional model and bycatch of stocks. weak lem these to benefit have weak a typically be are will fecundity hence reserves low and survivorship, with overfishing, high species from since risk However, at stocks. most ones fecundity the low in with are Species and (26). system (29) groundfish generally Coast West both the sur- fecundity, adult low high have with typically species vivorship so trade-offs, involve histories life All E 20% 40% 60% 80% biul,teeaebt te oeta ouin oteprob- the to solutions potential other both are there Obviously, 0% %2%60% 20% 0% o he yohtclseispis h persistence The pairs. species hypothetical three for ) PNAS | uut2,2017 22, August c 40% | o.114 vol. | o 34 no. | 8931

SUSTAINABILITY INAUGURAL ARTICLE SCIENCE AB

75% 75%

40% 40%

50% 50% 20%

20% 25% 25% 5%

Escapement Outside Reserve (E) Escapement Outside Reserve (E) 5%

0% 0%

0% 10% 20% 30% 40% 0% 10% 20% 30% 40% Reserve Size (c), Bocaccio Reserve Size (c), Darkblotched CD

75% 75% 40% 40%

20% 20%

50% 50% 5% 5%

25% 25% Escapement Outside Reserve (E) Escapement Outside Reserve (E)

0% 0%

0% 10% 20% 30% 40% 0% 10% 20% 30% 40% Reserve Size (c), Pacific Ocean Perch Reserve Size (c), Yelloweye

Fig. 2. Strong-stock yield (background color and circle size) and weak-stock persistence boundary (bold curves, representing 5, 20, or 40% of weak-stock carrying capacity) for combinations of reserve size (c) and strong-stock escapement outside the reserve (E) for the West Coast groundfish fishery, with Dover sole as the strong stock and four different weak stocks. Parameters are determined as described in Materials and Methods, based on the recent stock- assessment summary (26). See Fig. 1 for further description. Each panel has a different weak stock: bocaccio (A), darkblotched (B), Pacific Ocean perch (C), and yelloweye (D), with the same strong stock.

at lower stock levels outside reserves as compared with stock most economically beneficial. A full consideration of this prob- levels that would exist if management were solely limiting effort lem would require a model and approach that was far more without reserves. These two observations suggest that strategies detailed and specific and that would consequently have less gen- with some escapement outside reserves could turn out to be the eral applicability.

Table 1. Parameters used in Fig. 1 (hypothetical) and Fig. 2 (West Coast fisheries) Parameter Fig. 1A Fig. 1B Fig. 1C Fig. 2A Fig. 2B Fig. 2C Fig. 2D

aw 0.85 0.5 0.7 0.85 0.939 0.95 0.955 mw 1.6 1.4 2.5 1 1 1 1 αw 0.4 0.6 0.78 6.26 13.62 2.67 3.14 βw 5 5 5 825.8 204.05 3495.3 72.59 as 0.01 0.01 0.01 0.87 0.87 0.87 0.87 ms 8.5 8.5 8.5 1 1 1 1 αs 0.7 0.7 0.7 16 16 16 16 βs 20 20 20 23799 23799 23799 23799

8932 | www.pnas.org/cgi/doi/10.1073/pnas.1705169114 Hastings et al. Downloaded by guest on September 27, 2021 Downloaded by guest on September 27, 2021 1 elF,RbrsC 20)Bnfisbyn onais h seyefcso marine of effects fishery The boundaries: beyond popula- Benefits (2003) exploit CM Roberts reserves FR, Marine Gell (2005) 11. MH Carr DA, Siegel SD, Gaines B, Gaylord 10. 2 ebrL,e l 20)Pplto oesfrmrn eev ein retrospective A design: reserve marine for models Population (2003) al. et LR, Gerber 12. 3 ucadF ei A atnsA iglD(04 oadadnmcmetacommunity dynamic a Toward (2004) D Siegel A, Hastings SA, Levin F, Guichard 13. 5 atnsA osodL 19)Euvlnei il rmmrn eevsadtradi- and reserves marine from yield in Equivalence (1999) reserve LW does Botsford and A, work Hastings reserves Do 15. reserves: marine of impact The (2003) BS Halpern 14. ea adtsta ou nmain- on population protec- unfished focus the of that percentage to mandates some back legal at stocks recruit (iii) weak and young taining reserves; of closures, of smaller fraction even tion greater with marine persist a stocks allows since weak which help dispersal, more to larval older, reserves limited accumulate population (ii) to adults; spatial reserves (i) fecund allows of including: which benefits reserves, structure, the age marine enhance using further are management char- should real-world reserves three that by ignored acteristics have strat- management we management of since spatial conservative, superior benefits likely of broadly these multispecies merits a Moreover, realistic be the egy. more can about the reserves case in those setting, management, species exceeds nonspatial is single yield there vs. the the although in Thus, case, management. debate reserve nonspatial con- marine by are yields achievable the when Even in guar- stocks. that weak max- strained closures of combinations, spatial persistence history by the life compromised antee not of have are range challeng- yields we wide imum these a though, for in importantly, that, More yields shown situations. higher weak-stock produce ing carrying can of reserves 40–50% marine (of stocks stocks, weak weak of of persistence capacity). populations suffi- only are high not they is that guarantee but area possible to quite fishable large is the it ciently of fishing), (∼50% trawl to size fishery per- off-limits their stock the weak to given to of Indeed, monitored contribute they sistence. part appropriately which to they as extent the are designed determine nor not system, were management How- closures already conservation. actually these rockfish has ever, for fishery closures incentives that significant economic ironically, established to by Somewhat led motivated 30). has selectivity (24, share should in catch We sys- multispecies advances general. the this in great that system for suggests however, of tool kind out, strongly management this point model and superior particular, our a selective in of be tem very may import not reserves general typically that the was gear (high- Thus, longest-lived the (8). the and among the survivorship), case, all this est are In stocks 2). (Fig. (overfished) results weak our of importance the illustrates atnse al. et Hastings .HladD,Jno E(02 yac ikposfrteU etCatgroundfish paradigms new Coast Will century: West twenty-first US the in the management Fisheries for (1999) pools J Caddy risk Bycatch 9. (2012) JE Jannot DS, Holland 8. (1957) RJ Beverton 7. fol- assemblage fish surf-zone management a of contrasting recovery for under Evidence (1991) prospects C Attwood fishery B, Bennett Global 6. (2016) al. et C, Costello 5. .Csel ,Gie D yhmJ(08 a ac hrspeetfihre collapse? fisheries prevent shares catch Can (2008) J man- Lynham fisheries SD, traditional Gaines of C, success Costello the on 4. Reflections (2014) D fisheries. Ovando unassessed world’s R, the Hilborn for solutions 3. and Status (2012) al. et fisheries. C, global Rebuilding Costello (2009) al. 2. et B, Worm 1. ehv hw htsailmngmn sn permanent using management spatial that shown have We States United the of Coast West the off fishery groundfish The reserves. yields. fisheries improving potentially in 2180–2191. history life and structure tion apply? fishery. 19. Vol London), Office, tionery Africa. South of coast southern the Ser on Prog reserve Ecol marine Mar a of establishment the lowing regimes. n rsetv synthesis. prospective and Science agement. ence praht aiersretheory. reserve marine to approach inlfihre management. fisheries tional matter? size 338:517–520. e ihBo Fish Biol Fish Rev clEcon Ecol 321:1678–1681. rcNt cdSiUSA Sci Acad Natl Proc rnsEo Evol Ecol Trends CSJMrSci Mar J ICES clAppl Ecol 78:132–147. 75:173–181. nteDnmc fEpotdFs Populations Fish Exploited of Dynamics the On 13:117–137. 71:1040–1046. 9:1–43. 18:448–455. clAppl Ecol Science 113:5125–5129. BioScience 13:47–64. 284:1537–1538. 54:1003–1011. Science 325:578–585. HrMjsysSta- Majesty’s (Her clAppl Ecol Sci- 15: 8 botJ,WlnJ 20)Rglto ffihre yac ihcmo-oloutput common-pool with bycatch fisheries of Regulation (2009) JE Wilen JK, Abbott solutions. 28. and Problems By-catch: (2000) KI Metuzals DL, Alverson MA, Hall 27. (2016) Council Management Fishery Pacific The 26. Plag 25. man- spatial Real-time (2015) CT Marshall DS, Holland R, Hilborn CL, Needle AS, Little 24. life multistanza of Representation (2010) K Rose W, Walters V, Christensen C, Walters hurdles. and Insights 23. areas: protected aspects marine Modelling fishery (2015) and al. et biodiversity EA, the Fulton assessing for 22. framework protected A (2009) marine al. on et depend PS, outcomes Levin conservation 21. Global (2014) al. et GJ, Edgar reserves. marine 20. and fisheries sustainable uncertainties, Irreducible (2000) M Mangel networks reserve 19. marine Designing (2010) SR Palumbi MH, Carr C, White SD, Gaines 18. single-species on improvement an models multispecies Are (2000) al. et AB, Hollowed 17. 6 atnsA osodL 20)Cmaigdsgso aiersre o fisheries for reserves marine of designs Comparing (2003) LW Botsford A, Hastings 16. rga) ..adSDG eespotdb h at aiyFoundation. W. Family Waitt (Biocomplexity Andrew the by Foundation the supported Science were Foundation, S.D.G. National and Moore Packard C.C. the program). Lucille by Betty and and and and Foundation, David the Mellon OCE-0119976; Gordon Trusts, Charitable Grant the of Pew University Foundation, Biocomplexity from the S.D.G. to NSF to History subcontract grants Natural under a of campus; Davis, Museum Barbara American California, Santa DEB-0072909; the the Grant from NSF and A.H. by to California, funded of center Eco- University a for the Center Synthesis, National and the Analysis by logical supported Group, Working Reserves Marine in subplots seven ACKNOWLEDGMENTS. the of each for 2. parameters and 1 eight subscripted Figs. these stock, summarizes weak a the 1 requires representing simulation (four given parameters by any the run eight affect To of not conclusions. will total our the issues in these of but involved nature parameters, (32) general these issues of statistical use potential and are estimation there that recognize We Eq. in parameters the results, our change up not Thus, does Beverton– 31. that the ref. 15 in factor of given scaling form those a as our such to in formulae, parameters standard using the model calculate Holt can for they values we If the report, mortality. From female this average. and male the the lists use derive report we to The differ, (26) 2. Fig. summary in stock-assessment used recent parameters the from data used We Methods and Materials multispecies in benefits ecological contexts. and may economic outside, that broad management find fishery provide we target sensible reserves, Overall, marine with species. well-designed combined be using pelagic by only fisheries most may of persis- the management constraint habi- stock for movement of weak challenge this guarantee fraction a large, to the relatively reserves is Since marine tence reserves. in the needed of protection tat receive bounds reserves to marine the enough of sedentary within benefits are these adults we of unless criterion none accrue course, persistence Of restriction used. less have the than rather density, and quotas. Bull Evaluation OR). Fishery Portland, Council, and Assessment Stock Fishery: complexity. intermediate of models using applications cal and Europe from Experiences discards: States. and United bycatch the reduce to approaches agement interaction trophic ecosystem of organization patterns. spatial for models ecospace in histories Sci Biol B Lond Soc R Trans reserves. marine of features. key five with areas Res Ecol Evol management. 18293. fisheries and conservation both for ecosystems? marine on impacts fishing 707–719. measuring for models n o biodiversity. for and a ecluae as calculated be can w n orrpeetn h togsok usrpe by subscripted stock, strong the representing four and , anyi 41:204–219. ´ nio cnManage Econ Environ J E ta.(04 utseisfihre aaeetadcnevto:Tacti- conservation: and management fisheries Multispecies (2014) al. et EE, ´ ulMrSci Mar Bull 2:547–557. ihFish Fish plEcol Appl J clAppl Ecol PNAS 86:439–459. hswr a upre hog h Designing the through supported was work This 370:20140278. 16:576–602. Nature | β 13:65–70. 46:735–742. α 57:195–204. uut2,2017 22, August = = 506:216–220. R 4h/(1 0 5h ∗ (1 − − − 1 ttso h aicCatGroundfish Coast Pacific the of Status h) h) rcNt cdSiUSA Sci Acad Natl Proc TePcfi ihr Management Fishery Pacific (The | R 0 o.114 vol. n steepness and ihFish Fish | CSJMrSci Mar J ICES 15:1–22. o 34 no. h 107:18286– a Pollut Mar .Table s). ie in given | Philos 8933 [19] [18] 57:

SUSTAINABILITY INAUGURAL ARTICLE SCIENCE 29. Cole LC (1954) The population consequences of life history phenomena. Q Rev Biol 31. Dorn MW (2002) Advice on west coast rockfish harvest rates from Bayesian meta- 29:103–137. analysis of stock- recruit relationships. N Am J Fish Manag 22:280–300. 30. Miller SJ, Deacon RT (2016) Protecting marine ecosystems: Regulation versus market 32. Mangel M, et al. (2013) A perspective on steepness, reference points, and stock assess- incentives. Mar Resource Econ 32:83–107. ment. Can J Fish Aquat Sci 70:930–940.

8934 | www.pnas.org/cgi/doi/10.1073/pnas.1705169114 Hastings et al. Downloaded by guest on September 27, 2021