Size-based species interactions shape herring and cod population dynamics in the face of exploitation

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1 Size-based species interactions shape herring and cod population dynamics in the face of exploitation P. DANIËL VANDENDEREN 1,2, AND TOBIAS VAN KOOTEN 1 1 Wageningen Institute for Marine Resources and Ecosystem Studies (IMARES), P.O. Box 68, 1970 AB IJmuiden, The Netherlands 2 Aquaculture and Fisheries, Wageningen University, P.O. Box 338, 6700 AH Wageningen, The Netherlands Citation: van Denderen, P. D., and T. van Kooten Size-based species interactions shape herring and cod population dynamics in the face of exploitation. Ecosphere 4(10): Abstract. Size-specific competition and predation interactions often link the population dynamics of fish species in their response to exploitation. The effects of harvesting on interacting fish species is of increasing relevance as more and more fish populations worldwide are reduced by fishing. When stocks are harvested, effects of harvesting may percolate to populations of other species with which it interacts through competition, predation, etcetera. When multiple species are exploited, this can lead to interactions between fisheries, mediated by ecological interactions. Nevertheless, most fish stocks are managed using a single-species framework. We studied how single-species explanations of historical population dynamics work out when size-based interactions between harvested species are taken into account. We have taken as a case study the dynamics of cod (Gadus morhua) and herring (Clupea harengus) in the North Sea. These dynamics are generally considered to be shaped by fishing pressure on and food availability to single species. Our results indicate that the explanatory power of these factors is maintained with the inclusion of species interactions, but the processes leading to the observed patterns are altered as the fates of the species are interdependent. The sign and magnitude of the interaction between the species depends on the state of the populations, their exploitation history and environmental factors such as resource productivity. This context-dependent response to changing fishery intensity has important ramifications for management. We show that management plans for the exploitation of either one of these species, or for the recovery of North Sea cod, which do not account for these subtle interactions, may fail or backfire. Hence, such interactions link the fate of these species in complex ways, which must be taken into consideration for successful management of their exploitation, including harvesting at maximum sustainable yield, as we move towards an ecosystem-based management of marine fisheries. Key words: alternative stable states; Clupea harengus; community dynamics; gadoid outburst; Gadus morhua; maximum sustainable yield; North Sea; size-selective predation; stage-structured model. Received 7 May 2013; revised 3 September 2013; accepted 5 September 2013; published 31 October Corresponding Editor: E. García-Berthou. Copyright: Ó 2013 van Denderen and van Kooten. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. daniel.vandenderen@wur.nl INTRODUCTION Management of exploited fish populations is often based on short-term predictions from single-species models (Quinn and Collie 2005, Beddington et al. 2007). However, with fishing intensifying worldwide, it is becoming increasingly obvious that the single species in isolation assumption is untenable. Organisms that are fished out of an ecosystem no longer compete, serve as prey, or fulfill any of the ecological function they may have had. Hence, as fishing reduces species to below their natural abundances, effects may percolate through the food web to v 1 October 2013 v Volume 4(10) v Article 130

2 species which are not directly targeted by the fishery. In recent years, there has been a move towards an ecosystem based management of marine fisheries (Botsford et al. 1997, Pikitch et al. 2004). Embracing the principle that exploiting fish species may affect the entire ecosystem of which the species are a part, also implies that when two or more species in an ecosystem are exploited, the fisheries may interact through the ecological relationships that may exist between the target species. We use a community model to study how the ecological interaction between two exploited species may have contributed to the observed historical dynamics of these stocks. Fish generally grow orders of magnitude over ontogeny (Werner and Gilliam 1984). Some approaches to modeling marine fish community completely forego the species concept, and model only a distribution of individuals with a certain body size (e.g., Benoît and Rochet 2004 and references therein). On the other hand, studies of models of interacting species show that sizedependent species interactions can induce the presence of alternative stable states and lead to species extinctions (Diehl and Feissel 2001, Mylius et al. 2001, Schellekens et al. 2010). Predators which feed only on certain life stages of their prey can, when harvested, exhibit an allee effect which emerges from indirect effects of the predator feeding on the prey population (Van Kooten et al. 2005). Such a size-specific predator can even facilitate competing predators which feed on different life stages of the same prey population (De Roos et al. 2008a). However, these results are derived in simple conceptual food webs (but see Van Leeuwen et al. 2008). We construct, based on documented size-based interactions, a model of two stage-structured consumers and their resource populations. We use cod (Gadus morhua) and herring (Clupea harengus) in the North Sea, which have been extensively studied, managed and harvested since the late 1960s. In this system, we examine whether the arguments which are used to explain the historical dynamics of each of these stocks in isolation, hold when the effects of stage-based competition and predation are taken into account. Historical population dynamics of cod and herring in the North Sea (Fig. 1) are often Fig. 1. Changes in spawning stock biomass (SBB) (A), recruitment (abundance of 1 year-old fish) (B) and annual fishing mortality rates (C) for herring (grey) and cod (black) in the North Sea between The roman numerals denote different phases in the dynamics of the two species. Cod data, between , is obtained from the single species assessment of ICES (2011a) and before 1963 extracted from figures from Pope and Macer (1996). Herring data, between , is obtained from the single species assessment of ICES (2011b) and before 1960 from Nash and Dickey-Collas (2005). explained in terms of changes in fishing intensity and resource productivity. North Sea herring became severly depleted in the late 1960s and 1970s, which is generally attributed to a combination of intense herring fishery and failed v 2 October 2013 v Volume 4(10) v Article 130

3 recruitment (Fig. 1, II) (Bjørndal and Conrad 1987, Dickey-Collas et al. 2010). To allow the herring stock to recover, a ban on herring fisheries in the North Sea was imposed in 1977, after which the population recovered. In 1980, regulated fishing was resumed (Fig. 1, III) and herring abundance continued to increase to higher levels, most likely as a result of careful management preventing overfishing (Fig. 1, IV) (Dickey-Collas et al. 2010). Simultaneously with the depletion in the herring stock in the late 1960s and 1970s, the cod population increased substantially, a period often referred to as the gadoid outburst (Fig. 1, II) (Horwood et al. 2006). The abundance of cod led to an increasingly high fishing intensity. Eventually, the spawning population of cod declined (Fig. 1, III). In addition to intense fishing, increased temperatures and shifts in plankton productivity have been shown to be important factors influencing the dynamics of North Sea cod (Beaugrand et al. 2003, Clark et al. 2003). The prevailing explanation of these timeseries is largely based on mechanisms affecting each of the species independently. There is however ample evidence for species interactions between cod and herring. The nursery grounds of juvenile cod and herring overlap in space (Daewel et al. 2011, Röckmann et al. 2011). Juveniles share part of their diet, so that resource competition may occur in early life stages (Fig. 2, I and II). Adults of cod and herring do not compete for the same resources (Fig. 2, III and IV). Cod is one of the top predators in the North Sea, feeding on a wide range of fish species, including herring (Pinnegar and Stafford 2007, ICES 2012) (Fig. 2, V and VI). Herring, in turn, feed on cod eggs when other prey, small crustaceans such as copepods and amphipods, is less abundant. Fish egg are mostly eaten by young herring, ages 2 3 years (Daan et al. 1985) (Fig. 2, VII and VIII). The emerging food web model (Fig. 2) contains elements of existing models of size-dependent mortality and predation (Van Kooten et al. 2005, Van Kooten et al. 2007) and of different variations of intraguild predation, life history omnivory and mutual predation (Holt and Polis 1997, Mylius et al. 2001, HilleRisLambers et al. 2006, Schellekens et al. 2010). There is also statistical evidence that cod and herring abundances in the North Sea covary. Both the abundance of adult cod and cod Fig. 2. Feeding relationship between juvenile and adult cod (C j, C a ) and juvenile and adult herring (H j, H a ) and their alternative resources (R j, R Ca, R Ha ). Roman numerals represent specific interactions and are explained in the main text. Fishery on both adult cod and adult herring is illustrated by F Ca and F Ha, respectively. recruitment show negative correlations with the biomass of the spawning population of herring (Dickey-Collas et al. 2010, Fauchald 2010). In the explanation of the historical dynamics of the two species based on fishing intensity and changes in resource productivity, these documented interactions are not taken into account, even though each on its own has the potential to change the effect of fishing. A final interaction which we have omitted in this study is cannibalism in cod (Neuenfeldt and Koster 2000, ICES 2012), because it is generally documented as a purely opportunistic interaction with consequences only for mortality of the victims, in which case the effects on population dynamics are limited (Claessen et al. 2004). Our study reveals additional mechanisms, resulting from the added species interactions, which can explain some of the historically observed patterns of herring and cod dynamics in the North Sea. The effects of these size-specific species interactions depend on the state of the populations, their exploitation history and environmental factors such as resource productivity. Our work shows that, although subtle and complex, these interactions are important factors determining the effects of exploitation and v 3 October 2013 v Volume 4(10) v Article 130

4 management, of either of these species. These results highlight the importance of intraspecific variation among life stages in transition from single-species to ecosystem-based management of marine fisheries. METHOD Model description Ecological effects on herring and cod dynamics were examined by using a stage-structured predator-prey-resource model. Fluctuations of cod and herring are generally considered in relation to fishing intensity and changes in resource productivity on single species. We show how these single-species drivers work out in our stage-structured multi-species model. This model framework is designed to yield stage-structured models describing biomass abundance, in such a way that its dynamical properties approximate those of a more complex fully size-structured model (De Roos et al. 2007, 2008b). The original model derivation does not incorporate predation mortality, but this can be implemented with a small modification similar to Van Leeuwen et al. (2008). Herring and cod each have a juvenile (immature) and an adult (mature) life-history stage (Fig. 2). Juveniles of both species feed on the same resource and therefore interspecific competition for food occurs among the juvenile stages. Adults of both species each have their own resource population so that interspecific resource competition does not occur. The dynamics of the three resources (R j, R Ca, R Ha ), juvenile (C j ) and adult cod (C a ) and juvenile (H j ) and adult herring (H a ) are described by the following ordinary differential equations: dc j dt dc a dt ¼ t þ Ca ði CaÞC a þ t Cj ði Cj ÞC j c C ðt þ Cj ði CjÞÞC j l Cj C j ¼ t Ca ði Ca ÞC a t þ Ca ði CaÞC a þ c C ðt þ Cj ði CjÞÞC j l Ca C a ð1þ ð2þ dh j dt dh a dt dr w dt ¼ t þ Ha ði HaÞH a þ t Hj ði Hj ÞH j c H ðt þ Hj ði HjÞÞH j l Hj H j ¼ t Ha ði Ha ÞH a t þ Ha ði HaÞH a þ c H ðt þ Hj ði HjÞÞH j l Ha H a ¼ d w ðr maxw R w Þ G w where w 2ðj; Ca; HaÞ: ð3þ ð4þ ð5þ Resources for both species cover a complex assembly of prey species and sizes, of which only a fraction is available as food for the fish (Beaugrand et al. 2003, Segers et al and references therein) and follow for that reason semi-chemostat dynamics (Persson et al. 1998), with turnover rate d w and maximum resource density R maxw. In this formulation, resource productivity is described by the product R maxw d w. Both juveniles and adults consume resources at rate G. This rate depends on both the resource and consumer densities, but the notation is abbreviated for clarity. Each stage of herring and cod have a net biomass production t x (I x ), which depends on the food intake rate (I x ) and the efficiency with which food is assimilated r, minus the mass specific metabolic rate (T x ): t x ði x Þ¼rI x T x where x 2ðC j ; C a ; H j ; H a Þ: ð6þ This quantity can become negative when food is scarce and intake very low. Under these conditions, biomass loss occurs equal to the deficit between intake and metabolic costs. To ensure that maturation and reproduction processes do not reverse (so that for example the juvenile stage loses biomass when the adults starve), the terms t a þ (I a ) and c(t j þ (I j )) are used, to denote max(0, t a (I a )) and max(0, c(t j þ (I j ))). With this formulation, maturation and reproduction can never become negative (De Roos et al. 2008b). The model framework requires the assumption that adults have reached their asymptotic size, and do not grow further. Instead, all adult net biomass production (t Ca (I Ca ) and t Ha (I Ha )) is used v 4 October 2013 v Volume 4(10) v Article 130

5 Table 1. Model parameters and their values. Parameter Value Unit Description Individual energetics T Cj day 1 Metabolic rate of juvenile cod T Ca day 1 Metabolic rate of adult cod M Cj 0.08 day 1 Maximum ingestion rate of juvenile cod M Ca day 1 Maximum ingestion rate of adult cod T Hj 0.03 day 1 Metabolic rate of juvenile herring T Ha 0.02 day 1 Metabolic rate of adult herring M Hj 0.16 day 1 Maximum ingestion rate of juvenile herring M Ha day 1 Maximum ingestion rate of adult herring r Assimilation efficiency of herring and juvenile cod r p Assimilation efficiency of adult cod Mortality l day 1 Background mortality of cod and herring F Ca varied... Fishing mortality of adult cod (as multiple of l ) F Ha varied... Fishing mortality of adult herring (as multiple of l ) Body size ratios z C Ratio between individual weight at birth and at maturation for cod z H Ratio between individual weight at birth and at maturation for herring Resource dynamics d 0.1 day 1 Resource turn-over rate R maxj varied... Maximum resource abundance for juvenile herring and cod R maxha Maximum resource abundance for adult herring R maxca 3... Maximum resource abundance for adult cod Cod-herring-resource interactions q Ca-. Hj Fraction spent foraging on juvenile herring by adult cod q Ca-. Ha Fraction spent foraging on adult herring by adult cod q Ha-. Cj Fraction spent foraging on juvenile cod by adult herring q Hj-. Cj Fraction spent foraging on juvenile cod by juvenile herring q Ca-. RCa Fraction spent foraging on adult cod resource by adult cod q Cj-. Rj 1... Fraction spent foraging on juvenile resource by juvenile cod q Ha-. RHa Fraction spent foraging on adult herring resource by adult herring q Hj-. Rj Fraction spent foraging on juvenile resource by juvenile herring for reproduction and hence added to the corresponding juvenile stage. The biomass abundance of adults only increases through maturation of juveniles (c C (t Cj (I Cj )) and c H (t Hj (I Hj ))), and decreases through adult mortality (l Ha and l Ca ). Apart from the inflow from reproduction, biomass abundance in the juvenile stages increases through somatic growth (t Cj (I Cj ) and t Hj (I Hj )). It decreases through maturation and juvenile mortality (l Hj and l Cj ). Under adverse food conditions, both the juvenile and adult stages lose biomass through starvation. Maturation in this model framework is a complex function which is derived in such a way that the equilibria of the model correspond with those of a more complex model with continuous size structure, rather than discrete stage-structure (De Roos et al. 2008b). Maturation depends on juvenile somatic growth and mortality, and on the ratio (z) between individual weight at birth and weight at maturation. Maturation for cod and herring is given by: c C ðt Cj ði Cj ÞÞ ¼ t CjðI Cj Þ l Cj 1 z 1 l Cj=t Cj ði Cj Þ C ð7þ c H ðt Hj ði Hj ÞÞ ¼ t HjðI Hj Þ l Hj : ð8þ 1 z 1 l Hj=t Hj ði Hj Þ H Herring is a fast-maturing species with, compared to cod, a small difference between size at birth and size at maturation (compare parameters z C and z H in Table 1). Individuals on average spend a relatively short time in the juvenile stage and require relatively little resources to mature. Consequently, the equilibrium density of herring is determined largely by resource competition among adults. We call the herring population in this state reproduction regulated because the resource limitation of per unit biomass reproductive output is the stabilizing process which keeps the population in equilibrium. Cod mature at larger size and later age than herring and hence show the inverse pattern: the equilibrium v 5 October 2013 v Volume 4(10) v Article 130

6 stage distribution of cod is determined largely by resource competition among juveniles. We call the cod population in this state maturation regulated because the resource limitation of per unit biomass maturation is the stabilizing process which keeps the population in equilibrium. Adults and juveniles of both species differ in their diet. Both adult cod and juvenile and adult herring have more than one food source and are assumed to divide their available foraging time among the different resources according to a factor q. The prey encounter rates of juvenile (E Cj ) and adult cod (E Ca ) and juvenile (E Hj ) and adult herring (E Ha ) depend on food densities and are described by: E Cj ¼ q Cj. Rj R j E Ca ¼ q Ca. RCa R Ca þ q Ca. Hj H j þ q Ca. Ha H a E Hj ¼ q Hj. Rj R j þ q Hj. Cj C j ð9þ ð10þ ð11þ E Ha ¼ q Ha. RHa R Ha þ q Ha. Cj C j ð12þ Note that the coefficient q represents a time budget breakdown, so the q values for each stage sum to unity. Factors q x-.y indicate the interaction strength of x feeding on y. Consumption follows a Holling type II functional response with a half-saturation constant equal to 1 (see Van Leeuwen et al. 2008) and maximum ingestion rate M: E x I x ¼ M x ð Þ 1 þ E x where x 2ðC j ; C a ; H j ; H a Þ: ð13þ With these intake rates we can define the combined mortality on the 3 resource populations as: E Cj G j ¼ M Cj ð ÞC j þ M Hj ð q Hj. RjR j ÞH j ð14þ 1 þ E Cj 1 þ E Hj G Ca ¼ M Ca ð q Ca. RCaR Ca 1 þ E Ca ÞC a ð15þ G Ha ¼ M Ha ð q Ha. RHaR Ha ÞH a ð16þ 1 þ E Ha Adult and juvenile mortality follow a similar expression and are based on the stage-independent (background) mortality l, fisheries mortality F and predation mortality, depending on the prey encounter rates: l Cj ¼ l þ M Ha q Ha. Cj 1 þ E Ha H a þ M Hj q Hj. Cj 1 þ E Hj H j ð17þ l Ca ¼ð1 þ F Ca Þl ð18þ l Hj ¼ l þ M Ca q Ca. Hj 1 þ E Ca C a ð19þ q Ca. Ha l Ha ¼ð1þF Ha Þl þ M Ca C a : ð20þ 1 þ E Ca Note that fisheries mortality applies only to adult stages and is modeled as a multiple of background mortality. Our model structure and parameterization (see below) reflects our aim of testing the community consequences of certain assumptions with regards to the ecological interactions between individuals, on the effects of changes in resource productivities and fishing mortality on the community. Neither the model nor the parameter values are an attempt to capture the ecological complexity of cod and herring living in the North Sea. In our results, we relate our communitylevel results, in terms of qualitative patterns, to the process-level assumptions we have put into the model. The software package Content (Kuznetsov et al. 1996) was used to numerically continue the equilibria of the system. Parameterization The vital rates and life history parameters of cod for our model are taken from Van Leeuwen et al. (2008). They use a model with more life stages to study the interaction between cod and sprat in the Baltic Sea. The derivation for the parameters of North Sea herring are described here. All parameter values are summarized in Table 1. Maintenance costs juvenile (T Hj ) and adult (T Ha ) herring. For larvae of Atlantic herring maintenance costs are estimated on 0.04 day 1 (Checkley 1984). It has been suggested that large adult herring have a maintenance cost of 0.02 day 1 (Rudstam et al. 1994). We assumed the maintenance costs in the juvenile stage to be between 0.04 day 1 and 0.02 day 1, resulting in the default value of T Hj 0.03 day 1. We used T Ha 0.02 day 1 v 6 October 2013 v Volume 4(10) v Article 130

7 as default value for the adult herring stage. Body size ratio herring (z H ). We used the body weight after metamorphosis as initial weight for the juvenile herring stage. This weight has been estimated at 0.84 g for North Sea herring by Heath et al. (1997). Weight at maturity was estimated from data from the herring assessment working group (ICES 2011c: combining table , North Sea herring weight at age in the stock, and , North Sea herring proportion mature at age 2). The estimated mean weight at maturity was 127 g, resulting in a ratio between initial and final size of herring of z H ¼ Maximum ingestion rate of juvenile herring (M Hj ). Heath et al. (1997) estimated that growth in North Sea juvenile herring from 0.84 g to 19.4 g will take approximately 185 days. This corresponds to a weight-specific growth rate (a Hj ), assuming that growth is exponential, of day 1. Although the growth range did not cover the whole juvenile herring stage, it is the most detailed description available and we therefore used this value to derive the maximum ingestion rate. The maximum ingestion rate was derived from: a Hj ¼ rm Hj T Hj, where r ¼ 0.3 and T Hj ¼ 0.03 (for T Hj see above), following Van Leeuwen et al. (2008). This corresponded to a maximum ingestion rate of M Hj ¼ 0.16 day 1. Maximum ingestion rate of adult herring (M Ha ). The same calculations as in Van Leeuwen et al. (2008) were used to estimate the maximum ingestion rate (M Ha ) for North Sea herring: A Ha ¼ j Ha (rm Ha T Ha ), where j Ha ¼ 0.8, r ¼ 0.3 and T Ha ¼ 0.02 (for T Ha see above). We derived the weight-specific growth rate (A Ha ) by examining the highest growth rates of herring between age 2 and 3 (71 93% mature, respectively). The mean weight had the highest increase between age 2 and 3 from 1998 to 1999, by a factor 1.59 (ICES 2011c: Table ). We could estimate A Ha by assuming that growth in weight was exponential: A Ha ¼ day 1. Based on these values, we could calculate M Ha : day 1. Despite the positive energy budget, herring cannot persist at this value in our model, as a result of other biomass loss factors (mortality). However, the maximum ingestion rate is underestimated since we did not calculate the maximum weightspecific growth rate but the highest increase in the whole population between age 2 and 3. We assume that the maximum ingestion rate is 10% higher than this day 1, resulting in a default value of day 1. Foraging effort allocation for herring and cod. The allocation of foraging effort to the different resources for each size class is generally unknown. We have chosen values in qualitative accordance with the literature and have included a detailed sensitivity analysis for the feeding interactions between herring and cod in Fig. 3. This analysis confirms that our results do not depend on the specific choice of parameter values but occur for a range of realistic values. RESULTS Impact of varying resource productivities With both species present, varying the productivity of the shared juvenile resource changes species dominance and reveals alternative stable states (Fig. 4). With increased juvenile resource productivity, we see an increasing numerical dominance of cod. This is somewhat counterintuitive, given that juvenile herring are better at feeding on the resource, because they have a larger maximum ingestion rate (Table 1). The results can be fully explained by considering a combination of life-history differences between cod and herring, and predation. An increase in productivity of the shared juvenile resource increases the abundance of juvenile and adult cod, and also leads to higher predation intensity on herring. As a result, adult herring density is reduced. Juvenile herring density increases, because the thinning out of the adult herring population results in an increase in the population reproduction rate of herring (Fig. 4D). With increasing juvenile resource productivity, an ever decreasing biomass of adult herring needs to supply an ever increasing population reproduction in order to balance the increasing mortality from predation. At some point, the compensation fails and there is too little adult biomass to maintain the necessary reproduction. This is the level of juvenile resource productivity at which the herring population collapses to low biomass abundance (around R maxj ; 12.4 with the parameters used in Fig. 4). The cod population profits from this collapse, because cod juveniles can now use virtually all juvenile resource. Resources for juvenile cod v 7 October 2013 v Volume 4(10) v Article 130

8 Fig. 3. Location of transition points between alternative stable states (solid lines) and persistence boundaries for cod and herring (dashed lines) as a function of the strength of the various predatory interactions: (A) predation of herring juveniles on cod juveniles (q Hj-.Cj ) vs. cod adults on herring juveniles (q Ca-.Hj ), (B) predation of q Hj-.Cj vs. cod adults on herring adults (q Ca-.Ha ) and (C) predation of q Hj-.Cj vs. herring adults on cod juveniles (q Ha-.Cj ). Two alternative stable states exist in the wedge-shaped area, where both herring and cod are present, and collapses from one state to the other can occur when the system is forced across these boundaries. The areas delimited by the dashed lines show where the fish species can persist. The wedge-shaped area exists in a range of parameter values of the feeding interactions between herring and cod. This shows that in a range of parameter values results will be supported without qualitatively affecting species dynamics. H, persistence of herring without cod. C þ H, stable two-species equilibrium. F Ha ¼ 0, F Ca ¼ 0, R maxj ¼ 14, all other parameters have default values. become so abundant that the population is no longer maturation regulated, but switches to a state where reproduction by adults regulates the population. In this equilibrium, adults are relatively abundant and juveniles relatively rare (Fig. 4A). Any further increase of juvenile resource productivity has relatively little effect (as compared with before the switch in the mode of regulation) on either cod or herring equilibrium abundance. This equilibrium reaches back to juvenile resource productivity values below those where the system switches, resulting in a range of juvenile productivity values for which alternative stable states occur. In the reproduction-regulated cod equilibrium, with decreasing juvenile resource productivity, a smaller and smaller biomass of adult cod needs to produce an increasing population reproduction in order to maintain high adult density in the face of reduced cod population maturation (Fig. 4C) in order to keep up the inflow of adults. Eventually (around R maxj ; 10.3 with the parameters used in Fig. 4), this compensation fails and the reproduction-regulated cod equilibrium goes extinct. At very low levels of juvenile resource productivity, the herring population benefits from its high feeding efficiency and can survive at productivities at which cod is extinct (Fig. 4, to the left of the vertical dashed lines). The shift in dominance induced by increasing juvenile resource productivity only occurs above a certain minimum productivity of the adult cod resource (R maxca ) (not shown). Below this threshold, adult cod cannot attain a high enough density to significantly influence the herring population, which is a necessity for the collapse of the herring population. Instead, the cod population gradually changes from a maturation regulated to a reproduction regulated state. A higher adult herring resource productivity (R maxha ), in contrast, strengthens the mechanism behind the hysteresis, moves the collapse of herring towards higher R maxj values (to the right in Fig. 4) and occurs at higher adult herring density (not shown). Impact of varying fishing mortality levels Starting in the high-productivity situation where cod is the dominant species (to the right of R maxj ; 12.4 in Fig. 4), increasing cod v 8 October 2013 v Volume 4(10) v Article 130

9 Fig. 4. Biomass and maturation and reproduction rates of cod and herring as function of juvenile resource productivity (expressed as maximum juvenile resource abundance (R maxj )). (A) Cod biomass (adult cod, red and juvenile cod, black); (B) herring biomass (adult herring, blue; juvenile herring, black); (C) cod reproduction (black) and maturation rate (grey); (D) herring reproduction (black) and maturation rate (grey). The vertical dashed lines show the boundary of the coexistence area. The solid lines correspond to stable equilibria, dashed lines to unstable equilibria. H, persistence of herring without cod. F Ha ¼ 0, F Ca ¼ 0, all other parameters have default values. harvesting mortality causes a limited decline in biomass and a simultaneous small increase in biomass of adult herring (Fig. 5A B, F Ca between 0 and 2.6), up to a threshold where the system switches to the herring-dominated equilibrium. At high juvenile resource productivity, growth of the cod population is regulated by the low reproductive output of the adult stage (Fig. 5C). The decline in adult density in response to a low harvesting mortality is small because it is compensated for by faster reproduction, leading to increased juvenile biomass of cod and subsequently increased maturation of juvenile cod (Fig. 5C). At some point, the maximum per unit biomass reproduction is reached, the compensatory mechanism fails and the adult cod population collapses. This collapse may occur at a range of juvenile resource productivities (Fig. 6). Fishery on maximum sustainable yield (MSY) for cod occurs when the population is on the verge of this collapse (Fig. 5D). The collapse allows herring to escape control by the adult cod and increase in abundance. The adult herring population always declines when herring fishing intensity increases. This decline is limited when herring is the dominant species and cod is present at low abundance. In this state, adult cod is unable to control the herring population because competition among juveniles limits cod maturation. Increased herring fisheries lead to higher juvenile herring abundance (Fig. 7B), further intensifying the v 9 October 2013 v Volume 4(10) v Article 130

10 Fig. 5. Increasing fishery mortality level on adult cod (F Ca ). (A) Cod biomass (adult cod, red and juvenile cod, black) as function of F Ca ; (B) herring biomass (adult herring, blue; juvenile herring, black) as function of F Ca ;(C) cod reproduction (black) and maturation rate (grey) as function of F Ca ; (D) the yield, the product of F Ca and the adult cod biomass, as function of F Ca. The vertical dashed lines show the boundary of the coexistence area. The solid lines correspond to stable equilibria, dashed lines to unstable equilibria. MSY, maximum sustainable yield; H, persistence of herring without cod. F Ha ¼ 0, R maxj ¼ 14, all other parameters have default values. competition between juvenile herring and cod. This leads to lower cod juvenile and adult abundance and hence lower herring predation mortality, which compensates for the increased fishing mortality. Eventually, the cod population is driven to extinction (Fig. 7A, to the right of the vertical dashes lines). This occurs at herring fishing intensity below that required for MSY (Fig. 7D). Finally, at high fishing intensity, the herring population switches to a state where maturation by juveniles regulates the population. DISCUSSION We investigated how the single-species explanations for the historical dynamics of cod and herring in the North Sea work out when the complex interplay of competition, food-dependent growth and reproduction, and mutual sizedependent predation are taken into account. Our results indicate that fishing effort and food availability remain important drivers for the population dynamics of both species, but the ecological coupling of the species reveals novel mechanisms leading to the observed species dynamics. These mechanisms are context-dependent, which has important ramifications for management. An important result of our work is that increased resource productivity does not necessarily translate into higher density of the most efficient competitor (herring) (Fig. 4), as it would v 10 October 2013 v Volume 4(10) v Article 130

11 Fig. 6. Location of transition points between alternative stable states (solid lines) and persistence boundaries for cod and herring (dashed lines) in relation to fishery mortality of adult cod (F Ca ) and resource productivity (expressed as maximum juvenile resource abundance (R maxj )).The solid lines correspond to the points in Fig. 4 and Fig. 5 at which one of the alternative stable states ceases to exist. Hence, in the wedge-shaped area between the solid lines, two alternative stable states exist where both herring and cod are present, and collapses from one state to the other can occur when the system is forced across these boundaries. The areas delimited by the dashed lines show where the fish species can persist. R: resource only, both fish species extinct. H, persistence of herring without cod. C þ H, stable two-species equilibrium. F Ha ¼ 0, all other parameters have default values. in a simple resource competition framework. The model shows that an increase in juvenile food leads to more juvenile and adult cod and eventually to a cod-dominated system. The positive relationship between juvenile resource productivity and juvenile cod is in line with earlier work (Beaugrand et al. 2003, Fauchald 2010), which shows a correlation between the most common zooplankton prey species and cod recruitment in the North Sea. We show that even when competition with more efficient competitors is taken into account, an increase in the juvenile resource productivity is still a plausible explanation for the gadoid outburst which occurred from the mid-60s until the mid-80s of the last century (Horwood et al. 2006). Our results predict a concurrent strong decline in herring density. The dynamics shown in Fig. 4 are similar to those described for an intraguild predation system with a stage-structured predator feeding on an unstructured consumer (Mylius et al. 2001), while the juvenile predator competes for resource with the consumer. The difference is that our intraguild prey (herring) collapses to low densities but never goes extinct. The decline in herring (Fig. 1, II) is usually attributed to high fishing mortality and failed recruitment (Bjørndal and Conrad 1987, Dickey- Collas et al. 2010). In the state where herring adults are abundant, we find only a marginal decline in herring from fishing (Fig. 7B). In the other equilibrium, at low adult herring density, the decline is more substantial (not shown). These results suggest that the collapse of herring in the 70s, where herring adults were high in abundance, may have been the result of not only the intense herring fishery, but also the indirect effects of the gadoid outburst itself. Our model suggests that this collapse of the herring population could have been a transition from a reproduction regulated to a maturation regulated state, which exists when cod is not excessively harvested and the juvenile resource is sufficiently productive (Fig. 6). This is in line with Nash et al. (2009), reporting a 10-fold increase in per capita offspring production in the years when North Sea herring was in what is generally considered to be a collapsed state (Dickey-Collas et al. 2010). They also found that high adult density, after the rebuilding of the herring population, resulted in a negative correlation between adult herring abundance and per capita number of offspring, which is indicative of a population regulated (kept in stable equilibrium) by the reproduction process (De Roos et al. 2007). During the rebuilding of the herring population, North Sea cod declined in abundance (Fig. 1A, I, II). Cook et al. (1997) suggested that the exploitation level of North Sea cod was unsustainably high from the mid-80s. Our model predicts that this would have reduced cod and increased herring abundance (Fig. 5A, B). The data (Fig. 1, III) shows no clear collapse of the cod population, as one would expect based on the model. However, the fishing pressure on herring also slowly built up over this period (Fig. 1C, I, II), which we predict to reduce the cod v 11 October 2013 v Volume 4(10) v Article 130

12 Fig. 7. Increasing fishery mortality level on adult herring (F Ha ) when cod is in the low density equilibrium. (A) Cod biomass (adult cod, red and juvenile cod, black) as function of F Ha ; (B) herring biomass (adult herring, blue; juvenile herring, black) as function of F Ha ; (C) herring reproduction (black) and maturation rate (grey) as function of F Ha ; (D) the yield, the product of F Ha and the adult herring biomass, as function of F Ha. The vertical dashed lines show the boundary of the coexistence area. The two alternative equilibrium levels of herring in isolation are connected by an unstable equilibrium (not shown for reasons of simplicity). Increased fishery on herring (to the right of F Ha ¼ 10) will decline herring towards extinction. MSY, maximum sustainable yield; H, persistence of herring without cod. F Ca ¼ 0, R maxj ¼ 9, all other parameters have default values. stock, weakening the dynamic coupling between cod and herring. An even further rebuilding of the herring population can possibly result in more predation on cod eggs and a negative impact on cod recruitment, so-called predator-pit dynamics (Bakun 2006). Analysis of a multi-species model (Speirs et al. 2010) confirmed that herring feeding on early life stages of cod can strongly impact cod abundance. This is consistent with Fauchald (2010) who suggests that harvesting herring may help to rebuild the reduced cod stock. Our results show the opposite when cod is in the low density equilibrium (which is most in line with the current historically low abundance in the North Sea): increasing fishing intensity on herring may lead to the extinction of the cod stock (Fig. 7A), even before herring harvesting on MSY (Fig. 7D), as it intensifies competition between juvenile cod and herring. In absence of competition among the juveniles of predator and prey, culling specific size-classes of the prey population might be an effective strategy for the recovery of the predator (Persson et al. 2007, Van Leeuwen et al. 2008). Our work shows that an increase in herring biomass can result in a strongly reduced reproduction (Figs. 4, 5, 7). This reduces competition among herring and cod juveniles leading to higher adult cod abundance. The result is a system where both species are present in v 12 October 2013 v Volume 4(10) v Article 130

13 relatively high adult biomass levels, like in the 1950s and 1960s (Fig. 1, I). This opposing prediction from our model is a result of our inclusion of resource competition among herring and cod juveniles and the assumption that the reproduction of adult herring depends on the abundance of its food. Which of the two possible responses to changes in herring abundances (an in- or decrease of cod) occurs in the North Sea cannot be determined based on our model. The potential effects of harvesting in food webs where certain life stages of the predator also compete for resources with the prey is clearly illustrated by the presence of a catastrophic collapse in the cod population in response to cod harvesting in our model. The current fisheries management for European Union waters is aimed at exploiting fish stocks at MSY. Our results for cod harvesting indicate the dangers of this approach: MSY for cod occurs when the population is on the verge of collapse (Fig. 5D). Coming from a situation with low fishing intensity, a management plan which annually increases fishing intensity as long as yield increases will almost inevitably push the cod population into the collapsed state, from which a substantial reduction in fishing pressure is needed to return to the high-abundance equilibrium. Once in the collapsed state (to the right of F Ca ; 2.6), a management plan which would prescribe a stepwise reduction in the harvesting intensity could get the population trapped in the local optimum which occurs at a higher harvesting intensity compared to that at which the real MSY occurs. A transition to this collapsed state can be induced by cod harvesting, an increase in juvenile resource productivity, or a combination of both (Fig. 6). Our work shows that the explanatory power of the single-species drivers is maintained with the inclusion of species interactions, but the processes leading to the observed patterns are altered as the fates of the species are interdependent. This interdependence introduces alternative stable states which have important implications for management and exploitation of these stocks. The continued application of the single-species management paradigm to these interacting species could well lead to mismanagement and depletion of either or both of the stocks. A shift to a multi-species approach is not enough as sizespecific interactions are largely overlooked in multi-species models (Irigoien and De Roos 2011), only resulting in a negative relationship between predator abundance and prey (see for example Kempf et al. (2010) for cod in the North Sea). We show that, although subtle and complex, size-specific interactions are important factors determining the effects of exploitation and management, of either of these species. Other studies have suggested the important role of such interactions (Byström et al. 1998, Speirs et al. 2010, Irigoien and De Roos 2011, Richardson et al. 2011), and our findings corroborate this: it is precisely these interactions which complicate the simple predator-prey interaction between the species, and which make that there is no simple negative relationship between the abundance of the predator and its prey. This illustrates that in order to successfully manage our seas and oceans, we need to look within species, at the various ecological interactions that individuals engage in as they spawn, grow up and reproduce. ACKNOWLEDGMENTS We thank M. Dickey-Collas, R. HilleRisLambers and A. D. Rijnsdorp for their help and support in this project and thank the anonymous reviewers for their helpful comments on earlier versions of this manuscript. This study was supported by the EU FP7 project MEECE (Marine Ecosystem Evolution in a Changing Environment). LITERATURE CITED Bakun, A Wasp-waist populations and marine ecosystem dynamics: navigating the predator pit topographies. Progress in Oceanography 68: Beaugrand, G., K. M. Brander, J. A. Lindley, S. Souissi, and P. C. Reid Plankton effect on cod recruitment in the North Sea. Nature 426: Beddington, J. R., D. J. Agnew, and C. W. Clark Current problems in the management of marine fisheries. Science 316: Benoît, E., and M.-J. Rochet A continuous model of biomass size spectra governed by predation and the effects of fishing on them. Journal of Theoretical Biology 226:9 21. Bjørndal, T., and J. M. Conrad The dynamics of an open access fishery. Canadian Journal of Economics 20: Botsford, L. W., J. C. Castilla, and C. H. Peterson v 13 October 2013 v Volume 4(10) v Article 130

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