On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing

For Review Only On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing. Journal: ICES Journal of Marine Science Manuscript ID: ICESJMS-2009-192.R2 Manuscript Types: Original Article Date Submitted by the Author: n/a Complete List of Authors: Solari, Aldo; Spanish Institute of Oceanography (IEO) Santamaría, María Teresa; Spanish Institute of Oceanography Borges, Maria-Fatima; Instituto de Investigação das Pescas e do Mar (IPIMAR/INRB) Santos, Miguel; Instituto de Investigação das Pescas e do Mar (IPIMAR/INRB) Mendes, Hugo; Instituto de Investigação das Pescas e do Mar (IPIMAR/INRB) Balguerías, Eduardo; Spanish Institute of Oceanography, Direction Díaz-Cordero, José; Spanish Institute of Oceanography Castro, José; University of Las Palmas, Fisheries Bas, Carles; Superior Council for Scientific Research (CSIC), Inst. Mar. Sc. Keyword: Sardina pilchardus, stock, recruitment, production, orbits of stability, dynamical continuum, variable carrying capacity, Iberian upwelling, sea surface temperature, environmental forcing http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science For Review Only On the dynamics of Sardina pilchardus: 1 orbits of stability and environmental forcing. 2 3 A. P. Solari (1,*), Mª T. G. Santamaría (2), Mª F. Borges (3), 4 A. M. P. Santos (3), H. Mendes (3), E. Balguerías (2), 5 J. A. Díaz Cordero (2), J. J. Castro (1) and C. Bas (4). 6 7 (1) University of Las Palmas de Gran Canaria (ULPGC); (2) Spanish 8 Oceanography Institute (IEO); (3) Portuguese National Institute of 9 Fisheries and Marine Research (IPIMAR); (4) Superior Council for 10 Scientific Research (CSIC, Barcelona). 11 12 (*) Address to corresponding author: Instituto Español de Oceanografía 13 (CECAF), Centro Oceanográfico de Canarias. Av. 3 de Mayo 73, 38005 14 Santa Cruz de Tenerife, Islas Canarias, España. Fax 34 922 54 95 54. 15 Email: <[email protected]>. 16 17 Abstract. 18 The dynamics of Sardina pilchardus in the Iberian upwelling area are 19 examined. Spawning stock biomass (SSB), recruitment (R) and production 20 (R/SSB) data for years 1978-2006 are analyzed in relation to both 21 Upwelling Index (UPW) and Sea Surface Temperature (SST). It is observed 22 that the population system oscillates in two relatively stable orbits (shown 23 Page 1 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – TEXT PART – p. 2/28 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE by multiresolution decomposition of the recruitment series) as the external 24 forcing (UPW and SST) are the inverse of one another, and, as the 25 synchrony is lost between both of the external variables, R and R/SSB shift 26 towards highly steep, negative (depensatory) trends. It is proposed that 27 such mechanics may have induced both recruitment failures and significant 28 decreases in abundance in the Iberian sardine stock. The observed 29 relationships are assumed to validate a complex dynamical continuum 30 (multiple orbits of stability) and variable carrying capacity, alternative 31 population model. Also, radial systems with two orbits of stability are 32 proposed for the R-SSB and S/SSB relationships. Results are discussed both 33 in relation to classical and alternative SR models in order to approach stock 34 rehabilitation and fishing mortality issues as the population shift toward 35 low recruitment and abundances. Finally, certain factors to consider in 36 exploitation strategies for systems with multiple orbits of stability are 37 discussed. 38 39 Key words. 40 Sardina pilchardus, stock, recruitment, production, orbits of stability, 41 dynamical continuum, variable carrying capacity, Iberian upwelling, sea 42 surface temperature, environmental forcing. 43 44 Page 2 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – TEXT PART – p. 3/28 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE Introduction. 45 Several authors have suggested possible links between stocks/populations 46 of small pelagic species (sardine and anchovies, for instance) and the 47 environmental forcing (i.e. upwelling intensity, climatic variability) and, 48 also, the difficulty to apply traditional population approaches which are 49 based on both a single equilibrium and an invariant carrying capacity. 50 Barange et al. (2009) argued both that (a) Small pelagic fish species are 51 characterized by marked fluctuations in numbers because of their high 52 dependence on highly variable, environmentally driven, annual recruitment 53 pulses and (b) These species, also, display low frequency, multi-decadal 54 productivity cycles. Also, it was suggested by Chavez et al. (2003) that (a) 55 There was an alternation of abundance between sardines and anchovies 56 which (b) cannot be explained by means of fishing pressure; (c) A 57 variability (seen as biological regime shifts) which could be linked to large-58 scale atmospheric or oceanic forcing at the basin level and (d) 59 Environmental forcings which act on multiple time scales. Furthermore, 60 Schwartzlose et al. (1999) suggested that (a) Sardine (S. sagax) and 61 anchovy (Engraulis spp.) fluctuate out of phase with each other as a 62 consequence of one or a few strong year classes are triggered rather than as 63 a response to a vacant niche; (b) Excessive fishing pressure on strong year 64 classes early in the recovery stage may prevent a species from assuming 65 Page 3 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – TEXT PART – p. 4/28 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE dominance so that the natural succession is influenced and (c) Near 66 simultaneous fluctuations of fish stocks in widely separated regions support 67 the view that they are sometimes influenced by climate operating at a 68 global scale. Moreover, Hsieh et al. (2009) suggested that the catches on 69 two anchovy species (E. heteroloba and E. punctifer) were mainly 70 determined by the abundance (strength) of E. japonicus whereas 71 relationships with environmental variables (water temperature and river 72 runoff) were transient. Also, Machu et al. (2009) suggested, as a result of a 73 coupled physical-biogeochemical modelling experiment, that recruitment 74 of sardines (S. pilchardus) could be related to the delay between high 75 abundance of plankton and favorable spawning conditions and Relvas et al. 76 (2009) observed (a) A generalized warming trend in the Canary upwelling 77 system (an important ground for sardine recruitment) and suggested both 78 that (b) significant decadal changes in the mesoscale patterns and (c) Such 79 a large-scale variability can reorganize communities and trophic 80 relationships. 81 82 Two of the most widely accepted frameworks used to describe the 83 theoretical relationship between parental stock and recruitment (also, 84 referred as the “SR” relationship/system) are the Beverton and Holt (1957) 85 and Ricker (1954) models (also, referred herein as “classical models”). 86 Page 4 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – TEXT PART – p. 5/28 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE These approaches were developed for the identification of the best 87 parameterization of the SR relationship. Their principal task was the 88 determination of the best mathematical function (shape and number of 89 parameters) which would permit better determination of coefficients 90 involving the fewest parameters. These classical models, which established 91 a general theoretical framework for modelling population dynamics in the 92 1950’s, consist of extinction curves where recruitment reaches either an 93 asymptotic maximum (Beverton-Holt) or becomes low at high spawning 94 stock sizes (Ricker). Both of these models were unified by Shepherd 95 (1982) whose functional form is given by 96 97 R S S K = ⋅ +    α δ 1 (1) 98 where R is recruitment, S is the spawning stock abundance and K the 99 threshold abundance above which density-dependent effects dominate (i.e. 100 the carrying capacity). The parameters α and δ are referred as the slope at 101 the origin and degree of compensation involved, respectively. The classical 102 dome-shaped (for δ > 1) and asymptotic (for δ = 1) functional forms 103 proposed by Ricker (1954) and Beverton-Holt (1957), respectively can be 104 Page 5 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – TEXT PART – p. 6/28 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE described within the same framework. An example for each of the models 105 with arbitrary parameter values is shown in Figure 1. 106 107 While the classical models provided important insights into population 108 dynamics and thus implied significant advances to fishery science, they are 109 tools with limited degrees of resolution (capacity to incorporate and 110 describe complex dynamics). Several authors (Clark (1976), Sharp et al. 111 (1983), De Angelis (1988), Fogarty (1993), Solari et al. (1997), Bas et al. 112 (1999)) have suggested that these models do not include key factors of 113 specific situations and have a limited capacity to link internal (population) 114 and external (environmental) dynamics. While such argumentation may 115 hold true, it may be fair to recall that the classical models were put forward 116 before any relevant ecological systems theory was proposed. 117 118 An alternative model. 119 From the classical models which proposed single equilibrium relationships 120 with an invariant carrying capacity, we developed an alternative general 121 framework for multi-oscillatory, dynamic systems in our earlier studies 122 (Solari et al., 1997, originally published in this journal; Bas et al., 1999; 123 Solari et al., 2003 and Solari, 2008). A new model was put forward in 124 which recruitment (to the population, area and fishery) is considered as a 125 Page 6 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – TEXT PART – p. 7/28 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE system (henceforth regarded as “system”) with dynamic features ranging 126 from chaos (the ceiling, when external conditions are extremely benign), 127 going through a range of relatively stable, converging cycles (as external 128 stress increases), to a quasi-standstill state with no clear oscillations (when 129 the minimum viable population is being approached). The proposed system 130 comprises of a dynamical continuum governed by a variable carrying 131 capacity with local dynamics in different orbits of stability (graphically 132 represented in Figure 2) and it is expressed as 133 134 , , 2 1 ( ) ( ) ( ) pop area fishery m i i i i a S R S S b c = ⋅ ≅ − + ∑ (2) 135 136 where recruitment, R, to the population (pop), area or fishery is defined as 137 a summation of non-linear functions of the adult stock (or stock-in-area), S, 138 and the entries i = 1 ... m represent the number of dynamical states (orbits 139 of stability and pseudo-equilibria) in the system, being m the highest 140 equilibrium where the relationship reaches the “ceiling” or maximum 141 allowable carrying capacity (Kmax). Pseudo-equilibria (Ei) are controlled by 142 the coefficients ai (slope of the curve at the origin), being bi and ci the 143 Page 7 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – TEXT PART – p. 8/28 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE density-dependent mortality entries. For instance, ai fulfils a similar 144 function to the natural rate of increase in the logistic equation. These 145 coefficients will define each equilibrium state and their values may be 146 fixed. Also, values of bi will define the ranges of stock for which pseudo-147 equilibria may arise. We use the concept of “pseudo-equilibria” as we 148 assume that the population system will show responses to an ever-149 changing environment, as well as the intrinsic density-dependent 150 processes, and thus “equilibrium values” will change rapidly. 151 152 Our proposed model was first in the literature to formalize the concepts of 153 (a) Variable carrying capacity and dynamical continuum as an expression 154 of the evolution of the population system which (b) could link all of the 155 known population mechanics (that is, density-dependent, density-156 independent and inverse-density-dependent processes) in a relatively 157 simple equation. Also, the framework allowed us to show dynamical 158 similarity at several spatio-temporal scales for case studies on skipjack 159 tuna, K. pelamis (Solari et al., 2003) and the common Octopus, O. vulgaris 160 (Solari, 2008). The system, which is limited by a maximum carrying 161 capacity and an overall minimum viable population (K0), is highly flexible 162 as it has the capacity to, persistently, evolve and return within a relatively 163 Page 8 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – TEXT PART – p. 15/28 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE window”, as proposed by Cury and Roy (1989). Linear trends are simple 288 regressions through the origin. 289 290 The phase planes of the external forcing (SST and UPW) and recruitment 291 (R, above left) and production (recruitment per spawning stock biomass, 292 R/SSB, right caption) for S. pilchardus in the Iberian upwelling zone, years 293 1978-2006 are shown in Figure 9 a-b. Both recruitment and production 294 show similar patterns: they oscillate in relatively stable orbits of stability 295 within certain ranges of SST and UPW beyond which the system shifts 296 toward steep negative trends. Series were standardized (Z), smoothed (S) 297 and log transformed (Log). Arrows show the direction of the trajectories. 298 Linear trends are simple regressions through the origin. 299 300 Also, we propose two further model options for the sardine dynamics in 301 the Iberian upwelling area. The phase planes showing two radial attractors 302 proposed for both recruitment and production per spawning stock biomass 303 for S. pilchardus in the Iberian upwelling zone, years 1978-2006 are shown 304 in Figure 10 a-b. Oscillations in relatively stable orbits may be governed 305 both by density-dependent processes and an environmental window which 306 may be represented by SST and UPW. S is spawning stock, Rec is 307 recruitment and simulation parameters and initial conditions were arbitrary. 308 Page 15 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – TEXT PART – p. 16/28 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE 309 Discussion. 310 Research on species such as sardine and anchovies is extensive. There are 311 factors affecting the dynamics of small pelagic species which suggest the 312 nonlinear, multivariate nature and complex interactions between density 313 dependent and density independent processes: decadal changes (Barange et 314 al. (2009), Relvas et al. (2009)), productivity cycles (Barange et al. (2009), 315 perturbations operating at several spatial scales, even at the basin-wide 316 scale (Chavez et al. (2003), Molinero et al. (2005)), transient relationships 317 (in abundances and catches; Hsieh et al. (2009), out-of-phase abundance 318 successions (Chavez et al. (2003), Hsieh et al. (2009)), delay between high 319 plankton production and recruitment (Machu et al. (2009), cascade 320 mechanisms (Molinero et al. (2005), among other features. Such evidence 321 may confirm that the multiple equilibriums paradigm is more appropriate in 322 aquatic ecosystems than the classical approach based on the existence of a 323 single stable equilibrium. 324 Hsieh et al. (2009) suggested that (a) Fluctuations of anchovy populations 325 might not simply be determined by any single but a nonlinear combination 326 environmental factors and (b) Fishing pressures and environmental changes 327 might have synergistically precipitated abundance declines. Also, Barangue 328 et al. (2009) argued that if out-of-phase sinusoidal trends in production 329 Page 16 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – TEXT PART – p. 17/28 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE exist, consequences may be important and management procedures 330 designed under such an assumption could be more effective than traditional 331 approaches. It was suggested that (a) The biological mechanisms behind 332 alternating cycles and space utilization may be more complex than a simple 333 replacement and (b) the evolution of sardine and anchovy populations may 334 be described by models based on climate driven habitat changes. 335 Furthermore, Molinero et al. (2005) pointed out that a cascade of links 336 between different (large and local) spatial scale climatic patterns (driven by 337 long-term temperature anomalies) affected the dynamics and top-down 338 effects exerted by jellyfish on copepods. Also, it was argued that such a 339 cascade of links should be integrated into the assessment and modelling 340 studies of pelagic ecosystems. 341 342 There are three main aspects in our paper which we would like to stress: (a) 343 Both recruitment and production (S. pilchardus in the Iberian upwelling) 344 appear to be related to an environmental window caused by oscillations in 345 both SST and UPW: the phase planes of stock, recruitment and production 346 oscillate in relatively stable orbits of stability for certain ranges of SST and 347 UPW within which both of the external variables are the inverse of one 348 another; once the synchrony in the sine-cosine, wave-like patterns between 349 the external variables is broken, the trajectories of both recruitment and 350 Page 17 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – TEXT PART – p. 18/28 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE production shift towards density-independent depensation and negative 351 growth occurs; if we are theoretically correct, we would, therefore, expect 352 both of the biological variables to adjust their temporal evolution onto 353 further pseudo-cycles once SST and UPW recover their “inverse 354 dynamics”; (b) Second, we put forward a new framework which may be 355 useful for the study and exploitation of S. pilchardus and other small 356 pelagics: invoking a multi-oscillatory system governed by a multivariate set 357 of external perturbations in which the orbits of stability in the population 358 are caused by inversely related overlapping relationships requires a highly 359 flexible framework; a multioscillatory system with two orbits (seen as 360 pseudo-cycles or radial attractors) can provide an alternative to describe the 361 observed dynamical system; (c) Third, although the classical models could 362 describe each of the orbits of stability as “discrete (unlinked) regimes”, 363 these models propose the concepts of an invariant carrying capacity and a 364 single equilibrium which is likely insufficient to describe such complex 365 dynamics; as we see it, to describe the sardine R and R/SSB system in 366 relation to SST and UPW, requires both a variable carrying capacity and a 367 dynamical continuum which may help to link both (alternatively, several) 368 orbits of (quasi)-stability together. 369 Also, the results presented herein may be supportive of the “optimal 370 environmental window” concept proposed for recruitment success in 371 Page 18 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – TEXT PART – p. 19/28 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE upwelling areas by Cury and Roy (1989): (a) the authors relate Ekman-type 372 upwelling, vertical advection, new inputs of nutrients and turbulence to 373 wind speed and, with food availability, they are considered factors that 374 affect larval survival and pelagic fish recruitment and (b) their results 375 showed that for Ekman-type upwelling the annual recruitment increases 376 with upwelling intensity until wind speed reaches certain critical values 377 beyond which recruitment decreases (for which they infer the existence of 378 the so called “optimal environmental window”). We reach a similar 379 inference using our own theoretical model. 380 381 Moreover, we go further in the non-linear analysis to show a variable 382 carrying capacity determined by certain ranges of the external forcing (SST 383 and UPW) outside of which recruitment and production shift from 384 relatively stable orbits of stability or pseudo-cycles toward density-385 independent depensation and, hence, negative population growth. 386 387 According to our criteria, there are certain critical factors to consider in 388 exploitation strategies for systems with multiple orbits of stability. There 389 are several key concepts spinning off from our alternative model that may 390 allow us to further investigate some of the aspects relating possible 391 sustainable exploitation strategies such as: (a) differential effects of fishing 392 Page 19 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – TEXT PART – p. 20/28 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE mortality: during density-dependent (intrinsic to the population) and 393 density-independent (environmentally induced) compensations (positive 394 growth) and depensations (negative growth), the impact of fisheries may be 395 different; and also, the negative impacts of fishing may be less during 396 compensatory phases; this implies that fishing pressure could be relatively 397 higher during compensations, depending on the current orbits of stability or 398 level of numbers; on the other hand, the consequences of high and intense 399 exploitation may be of a negative nature once the trajectory of the 400 population becomes depensatory (negative population growth); the 401 differential effects of fishing (positive and negative growths during both 402 density-dependent and density-independent processes) together with length 403 and degree of the slopes in the trends should be further investigated; (b) 404 Understanding of fishery collapses (or shifts to low orbits of stability with 405 low oscillations in numbers) due to depensatory processes induced by the 406 combined effects from the environment and high fishing mortality: the 407 highest negative impacts in the population may be expected during density-408 independent and density-dependent depensations operating simultaneously; 409 such processes may lead both recruitment and production towards low 410 levels from which a rehabilitation will not occur until a new environmental 411 pulse (“inverse dynamics” between SST and UPW) make it possible and 412 (c) Short and medium term estimation of recruitment due to trends (slopes 413 Page 20 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – TEXT PART – p. 21/28 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE and temporal evolution) in external “best descriptor” variables (such as 414 SST, SST Anomaly, SSTA, North Atlantic Oscillation, NAO, upwelling 415 strength, among others). 416 417 Also, our alternative model allows analysis of factors such as the high 418 variability in the data and determination of how combined, multivariate 419 correspondences, memory effects, time lags, periodic oscillations, noise 420 and sensitivity to external conditions may affect the population system. We 421 should further investigate whether there may be dynamical similarity at 422 several spatio-temporal scales and the potential extrapolation of trends 423 between different scales of changes in S. pilchardus. Clearly, the forward 424 and backwards bending nature of catches, fishing effort, and abundance, 425 and the incorporation of multivariate perturbations into the model and 426 aspects related to auto correlated residuals in population systems with 427 strong dependencies on pulses from wave-like external variables should be 428 taken into account. The flexibility of the theoretical framework we propose 429 and multiplicity of factors which may be incorporated into a relatively 430 simple model may be some of the advantages of our approach. 431 432 433 Page 21 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – TEXT PART – p. 22/28 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE Acknowledgements. 434 The present study was carried out within the framework of the 435 EUROCEANS concerted action on small pelagics (year 2008) at the 436 Portuguese National Institute of Fisheries and Marine Research (IPIMAR) 437 and, also, funded, in part, by the Ministry of Science and Innovation 438 (MICINN) of the Spanish Government. Both of the referees and Editor are 439 acknowledged for suggesting changes which improved both the 440 introduction and discussion sections in this paper. 441 442 443 444 445 446 447 448 449 450 451 452 453 454 Page 22 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – TEXT PART – p. 23/28 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE References. 455 Bakun, A. . 1996. Patterns in the ocean. Ocean processes and marine 456 population dynamics. California Sea Grant/CIB, La Jolla. 457 458 Barange, M., J. Coetzee, A. Takasuka, K. Hill, M. Gutierrez, Y. Oozeki, C. 459 van der Lingen, V. Agostini (2009). Habitat expansion and contraction in 460 anchovy and sardine populations. Progr. in Oceanogr. (In Press). 461 462 Bas, C, A. P. Solari and J. M. Martín . 1999. Considerations over a new 463 recruitment model for exploited fish populations. Royal Academy of 464 Sciences, Barcelona. Vol. LVIII, Num. 5:157-183. 465 466 Beverton, R. J. and S. J. Holt . 1957. On the dynamics of exploited fish 467 populations. Ministry of agriculture, fisheries and food (London). Fisheries 468 investigation series 2 (19). 469 470 Chavez, F. P., J. Ryan, S. E. Luch-Cota and M. Ñiquen (2003). From 471 Anchovies to Sardines and Back: Multidecadal Change in the Pacific 472 Ocean. Science 299:217-221. 473 474 Page 23 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – TEXT PART – p. 24/28 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE Clark, C. .1976. Mathematical Bio economics: The optimal management of 475 renewable resources. John Wiley and Sons Inc. 476 477 Cury, P. and C. Roy . 1989. Optimal environmental window and pelagic 478 fish recruitment success in upwelling areas. Can. J. of Fish. and Aq. Sc. 479 46(4):670-680. 480 481 De Angelis, D. L. . 1988. Strategies and difficulties of applying models to 482 aquatic populations food webs. Ecol. Modelling 43:57-73. 483 484 Fogarty, M. . 1993. Recruitment in randomly varying environments. ICES 485 J. Mar. Sci. 50:247-260. 486 487 ICES . 2007. Report of the Working Group on the assessment of Mackerel, 488 Horse Mackerel, Sardine and Anchovy. ICES CM 2007/ACFM:31 489 490 Hsieh C. H., C. S. Chen, T. S. Chiu, K. T. Lee, F. J. Shieh, H. Y. Pan and 491 M. A. Lee (2009). Time series analyses reveal transient relationships 492 between abundance of larval anchovy and environmental variables in the 493 coastal waters southwest of Taiwan. Fish. Oceanogr. 18(2):102-117. 494 495 Page 24 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – CAPTIONS PART – 3/10 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE 1980 1985 1990 1995 2000 2005 Year -2 0 2 ZS Log SSB Sardine -2 0 2 ZS Log R Sardine Fig. 3. The European sardine (Sardina pilchardus) recruitment (R) and spawning stock biomass (SSB), log transformed (Log), smoothed (S, bold line) and standardized (Z) series in the Iberian upwelling zone for years 1978-2006, as estimated by ICES (2007). Page 31 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – CAPTIONS PART – 4/10 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE 1980 1985 1990 1995 2000 2005 Year -2 0 2 Z S L o g R / S S B S a r d i n e Fig. 4. Production (recruitment per spawning stock biomass, R/SSB) of the European sardine (Sardina pilchardus) in the Iberian upwelling zone for years 1978-2006 (raw data after ICES, 2007). Series were log transformed (Log), smoothed (S, bold line) and standardized (Z). Page 32 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – CAPTIONS PART – 5/10 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE -2 -1 0 1 2 R/SSB (t) -2 0 2 R / S S B ( t + 1 ) Fig. 5. The phase plane of production (recruitment per spawning stock biomass, R/SSB) with lag 1 of the European sardine (Sardina pilchardus) in the Iberian upwelling zone for years 1978-2006. The original series were log transformed, smoothed and standardized. The dashed line is a linear regression through the origin. Page 33 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – CAPTIONS PART – 6/10 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE -2 -1 0 1 2 ZS Log Sardine SSB (t) -2 0 2 Z S L o g S a r d i n e R ( t + 1 ) A B Fig. 6. The stock and recruitment relationship in the European sardine (Sardina pilchardus) in the Iberian upwelling zone for years 1978-2006. Series were standardized (Z), smoothed (S, bold line) and log transformed (Log). The lag to recruitment is one year. The rectangle indicates the orbits of stability (A, B). The dashed lines is a simple regression through the origin. Page 34 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – CAPTIONS PART – 7/10 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE S2 D2 D1 sum 0 5 10 15 20 25 30 Fig. 7. The (S8) wavlet analysis (multiresolution decomposition, MRD) on the recruitment series on European sardine (Sardina pilchardus) from the Iberian upwelling zone for years 1978-2006. The dashed lines indicate the peaks for the sum of the signals and eight year (D1-D2) and smoothed, low frequency (S2) processes. Page 35 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – CAPTIONS PART – 8/10 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE 1975 1980 1985 1990 1995 2000 2005 Year -1 0 1 2 Z S L o g ( U p w . I n d e x , S S T ) Upw. SST Fig. 8. The Sea Surface Temperature (SST; with centre at 39.5º N and 9.5º W) and Ocean Coastal Upwelling Indices (UPW; latitude 43-37º N and longitude 9º W) for years 1978-2006 (after ICOADS/NOAA, 2007) series. Data values were standardized (Z), smoothed (S) and log transformed (Log). Page 36 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – CAPTIONS PART – 9/10 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE -1 0 1 2 ZS Log SST (----), ZS Log UPW (- - - -) -3 -2 -1 0 1 Z S L o g R S a r d i n e -1 0 1 2 ZS Log SST (----), ZS Log UPW (- - - -) -2 0 2 Z S L o g R / S S B S a r d i n e Fig. 9 a-b. Phase planes of the external forcing (Sea Surface Temperature, SST and Upwelling Index, UPW) and recruitment (R, above left) and production (recruitment per spawning stock biomass, R/SSB, right caption) for Sardina pilchardus in the Iberian upwlling zone, years 1978-2006. Series were standardized (Z), smoothed (S) and log transformed (Log). Arrows show the direction of the trajectories. Linear trends are simple regressions through the origin. Page 37 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 For Review Only “On the dynamics of Sardina pilchardus: orbits of stability and environmental forcing” A. P. Solari, Mª T. G. Santamaría, Mª F. Borges, A. M. P. Santos, H. Mendes, E. Balguerías, J. A. Díaz Cordero, J. J. Castro and C. Bas MS – CAPTIONS PART – 10/10 REVISED AS PER INSTRUCTIONS OF THE EDITOR AND REFEREE Rec1 i Rec2 i S1 i S2 i , Rec1 i Rec2 i S1 i S2 i , Fig. 10 a-b. The phase planes showing two radial attractors proposed for recruitment and production per spawning stock biomass for Sardina pilchardus in the Iberian upwlling zone, years 1978-2006. Oscillations in relatively stable orbits may be governed both by density-dependent processes and an environmental window which may be represented by Sea Surface Temperature and Upwelling Index. S is spawning stock, Rec is recruitment. Parameter values are arbitrary. [END OF CAPTIONS PART] Page 38 of 38 http://mc.manuscriptcentral.com/icesjms Manuscripts submitted to ICES Journal of Marine Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60