Progress in Oceanography Progress in Oceanography 74 (2007) 500–514

Progress in Oceanography Progress in Oceanography 74 (2007) 500–514 www.elsevier.com/locate/pocean

Modeling environmental eﬀects on the size-structured energy ﬂow through marine ecosystems. Part 2: Simulations

Olivier Maury *, Yunne-Jai Shin, Blaise Faugeras, Tamara Ben Ari, Francis Marsac

IRD (Institut de Recherche pour le De´veloppement) – UR 109 Thetis CRH, av. Jean Monnet, B.P. 171, 34203 Se`te cedex, France

Available online 13 May 2007

Abstract

Numerical simulations using a physiologically-based model of marine ecosystem size spectrum are conducted to study the influence of primary production and temperature on energy flux through marine ecosystems. In stable environmental conditions, the model converges toward a stationary linear log–log size-spectrum. In very productive ecosystems, the model predicts that small size classes are depleted by predation, leading to a curved size-spectrum. It is shown that the absolute level of primary production does not affect the slope of the stationary size-spectrum but has a nonlinear effect on its intercept and hence on the total biomass of consumer organisms (the carrying capacity). Three domains are distinguished: at low primary production, total biomass is independent from production changes because loss processes dominate dissipative processes (biological work); at high production, ecosystem biomass is proportional to primary production because dissipation dominates losses; an intermediate transition domain characterizes mid-production ecosystems. Our results enlighten the paradox of the very high ecosystem biomass/primary production ratios which are observed in poor oceanic regions. Thus, maximal dissipation (least action and low ecosystem biomass/primary production ratios) is reached at high primary production levels when the ecosystem is efficient in transferring energy from small sizes to large sizes. Conversely, least dissipation (most action and high ecosystem biomass/primary production ratios) characterizes the simulated ecosystem at low primary production levels when it is not efficient in dissipating energy. Increasing temperature causes enhanced predation mortality and decreases the intercept of the stationary size spectrum, i.e., the total ecosystem biomass. Total biomass varies as the inverse of the Arrhenius coefficient in the loss domain. This approximation is no longer true in the dissipation domain where nonlinear dissipation processes dominate over linear loss processes. Our results suggest that in a global warming context, at constant primary production, a 2–4 C warming would lead to a 20–43% decrease of ecosystem biomass in oligotrophic regions and to a 15–32% decrease of biomass in eutrophic regions. Oscillations of primary production or temperature induce waves which propagate along the size-spectrum and which amplify until a ‘‘resonant range’’ which depends on the period of the environmental oscillations. Small organisms oscillate in phase with producers and are bottom-up controlled by primary production oscillations. In the ‘‘resonant range’’, prey and predators oscillate out of phase with alternating periods of top-down and bottom-up controls. Large organisms are not influenced by bottom-up effects of high frequency phytoplankton variability or by oscillations of temperature. 2007 Elsevier Ltd. All rights reserved.

Keywords: Size spectrum; Numerical simulations; Carrying capacity; Environmental eﬀects; Bioenergetics; Energy ﬂow

* Corresponding author. E-mail address: [email protected] (O. Maury).

1. Introduction

Size-based analyses of marine ecosystems, where body size rather than taxonomic identity is considered as being the most important variable determining trophic interactions and metabolism, is a useful and comple- mentary alternative to species-based analyses (e.g., Jennings, 2005; Shin et al., 2005; Woodward et al., 2005). Size-based analyses of ecosystems rest on the idea that size is the most structuring dimension of ecological systems along which their dynamics can be projected. Thus, large individuals of small species are supposed to be functionally equivalent to small individuals of large species (Kerr and Dickie, 2001). This approximation is based on the fundamental observation that many ecological traits as well as metabolic processes are well correlated with body size (Sheldon et al., 1972; Blueweiss et al., 1978; Gillooly et al., 2001; Brown and Gillooly, 2003; Marquet et al., 2005; West and Brown, 2005; Woodward et al., 2005). Furthermore, because most predators are larger than their prey (Sheldon et al., 1972), predator–prey relationships are, in many marine systems, mostly determined by size (Lundvall et al., 1999; Scharf et al., 2000; Jennings et al., 2001 and Jennings et al., 2002; Shin and Cury, 2004). Because it captures the most important aspects of ecosystem functioning, body size is therefore used to synthesize a variety of co-varying traits into a single dimension (Cousins, 1980; Woodward et al., 2005). One of the most powerful metrics used by marine ecologists to conduct size-based analyses of aquatic food webs is the size spectrum, i.e., the distribution of the biomass of all organisms as a function of their body mass (e.g., Jennings, 2005). The size-spectrum reflects and synthesizes both complex trophic interactions between species where bottom-up as well as top down controls interfere continuously (e.g., Cury et al., 2003) and the transfer and dissipation of energy from primary producers to top predators. The slope of the size-spectrum appears to be remarkably conservative between different aquatic systems. This obviously reveals similar processes of ecosystems functioning (Boudreau and Dickie, 1992). Predation allows the transfer of solar energy through ecosystems, along food chains, whereas biological work (metabolic activity) allows for its dissipation. In this paper, we focus on the effects of variability and changes of primary production and temperature on the transfer and dissipation of energy through ecosystems by studying the size-spectrum of marine ecosystems. For that purpose, we use a numerical model of marine size-spectrum which is fully described in a companion paper (Maury et al., 2007). This model explicitly distinguishes primary producers from consumers and is based on a mass-balanced mechanistic approach taking into account essential ecological and physiological processes such as: size-based opportunistic trophic interactions, predators competition for prey, allocation of energy between growth and reproduction, somatic as well as maturity maintenance based on the Dynamic Energy Budget theory (Kooijman, 1986, 2000, 2001), size-dependent predation and starvation mortality, temperature dependence of organism’s physiological rates. Considering explicitly the physiological bases of metabolism, the main constraints which control trophic interactions and the size structured nature of those processes enable to represent the various modes of energy transfer through marine ecosystems and their response to environmental forcing. In stable environmental conditions and using a reference set of parameters derived from empirical studies, the model converges toward a stationary linear log–log size-spectrum with a slope equal to 1.06 which is consistent with the values reported in empirical studies (Maury et al., 2007). After a brief presentation of the hypotheses of the model, various simulations are conducted to analyze the effects of the environment on the size-spectrum and total biomass of the ecosystem. The effects of primary production and temperature levels are considered as well as the effects of their variability.

2. Model and simulations

2.1. The size-spectrum model

This section presents the set of hypotheses and ecological principles which form the basis of our model. Readers interested in a detailed description of its mathematical formulation should refer to the companion paper (Maury et al., 2007). 502 O. Maury et al. / Progress in Oceanography 74 (2007) 500–514

2.1.1. Notations and state variables 1 3 Our model deals with nt,w (J kg m ), the energy content of the marine ecosystem at time t and weight w 3 in 1 m of seawater. nt,w can easily be converted into the more usual ‘‘normalized biomass size-spectrum’’ using the mean energetic content of one unit of biomass w (J kg1) which is assumed to be a constant parameter. Our model focuses on both autotrophic producers and heterotrophic consumers, with a particular emphasis on consumers (Fig. 1). For the sake of simplicity, heterotrophic decomposers (mostly the bacterial loop) are not considered.

2.1.2. Producers dynamics To avoid an explicit modeling of phytoplankton growth and reproduction, the biomass of producers is assumed to be uniformly distributed over their size range. For simplicity, a source/sink equation is used, taking into account the primary production which enters the system, the nonpredatory mortality rate aﬀecting primary producers and the mortality rate due to the predation exerted by consumers.

2.1.3. Consumers dynamics The bio-ecological processes taken into account to model consumers are predation, mortality, assimilation and use of energy for maintenance, growth and reproduction. The equation used to describe the energy fluxes through the weight range of consumers combines a transport term representing growth, three sink terms for predatory, nonpredatory and starvation mortality and a source term accounting for reproduction (Eq. (1)). 8 > on oðc n Þ > t;w t;w t;w k Z M starv n < ot ¼ ow ð t;w þ w þ t;w Þ t;w ð1Þ > ct;w nt;wegg ¼ Rt :> egg 0 n0;w ¼ nw where t stands for time and w for weight, c (kg s1) is the growth rate, k (s1) is the mortality rate due to predation, Z (s1) is the loss of energy from the system due to nonpredatory mortality, Mstarv is the starvation 1 1 3 mortality rate (s ) and Rt (J s m ) is the input of eggs into the system due to reproduction which is taken into account in the boundary condition in w = wegg, the weight of eggs. To ensure a rigorous mass balance, all the coefficients of Eq. (1) are derived according to the principle of energy conservation. Predation corresponds to a loss of energy for preyed weight classes and a gain of energy for predating weight classes. It is supposed to be opportunistic and only controlled by a selectivity curve which is a function of the ratio of sizes between organisms. Hence, all organisms can be potentially predators and prey at the same time, depending on their relative sizes (Fig. 2). For a given predator, prey of a given weight are eaten in proportion to the ratio of their selected biomass over the biomass of all possible prey. A simplified version of the DEB (Dynamic Energy Budget) theory is used (Kooijman, 1986, 2000, 2001; Nisbet et al., 2000) to account for the basic physiological processes involved in the acquisition and use of energy by organisms. The amount of energy ingested by a predator is supposed to be proportional to a

ξ t,w

Primary producers Consumers

0 w1wegg wmax Weight

Fig. 1. Schematic representation of the modeled ecosystem distinguishing primary phytoplanktonic producers from predatory consumers (log–log). O. Maury et al. / Progress in Oceanography 74 (2007) 500–514 503

0.8 Prey too large Prey too small Prey selectivity curves 0.6

0.4 Prey selection

0.2

0 0 0.2 0.4 0.6 0.8 1 1.2 Prey size (m)

Fig. 2. Limitation curves for preys too large to be ingested (black dots), preys too small to be ingested (open circles) and resulting prey selectivity function as a function of prey length for a 2 m long predator.

body surface (the squared length of organisms) and related to the amount of prey with a Holling type II functional response. The ingested energy is supposed to be used in the same way by any organism: it is assimilated at a given cost, then a fraction j is used for somatic growth and maintenance whereas a fraction (1 j) is allocated to egg production and gonadic maintenance (Fig. 3). The energetic cost of growth is explicitly considered in the balance equations and the eggs produced are injected at the basis of the size- range of consumers. In our model, growth in length and egg production cannot be negative. When maintenance expenses exceed food intake, growth and/or reproduction cease and a starvation mortality term ensures that mass conservation is properly respected. Hence, starvation is a net dissipation of energy at the ecosystem level. Mortality for other causes than predation (diseases, ageing, etc.) is simply supposed to be a decreasing allometric function. In our model, the Arrhenius temperature-dependent correction factor is used to correct ingestion rate, maintenance rate, nonpredatory mortality rate and swimming speed. The Arrhenius temperature-dependent correction factor account for temperature effects on the physiological rates of organisms at the intra-specific level (Kooijman, 2000; Clarke and Fraser, 2004). It does not keep a mechanistic meaning at the inter-specific level (Clarke, 2004; Clarke and Fraser, 2004) but it still provides a good statistical description of temperature effects on metabolic rates at the ecosystem level, even if purely chemical effects are altered by complex eco-evolutionary processes acting at this scale (Clarke and Johnston, 1999; Gillooly et al., 2001, 2002; Enquist et al., 2003; Clarke, 2004; Clarke and Fraser, 2004).

ORGANISM

Structure growth somatic κ growth maintenance K ingestion assimilation PREY gonadic 1-κ maintenance reproduction 1-K reproduction

Eggs

Fig. 3. Schematic representation of energy ﬂow through organisms (simpliﬁed from Kooijman, 2000). 504 O. Maury et al. / Progress in Oceanography 74 (2007) 500–514

2.2. Simulation experiments

In a first set of simulations, the effects of varying primary production are explored. The reference values of the parameters (TableR 1 in Maury et al., 2007) are used. The stationary size-spectrum as well as its associated 1 wmax total biomass ðw x¼0 nt;xdxÞ are computed for several levels of primary production (P expressed in Jday1 m3) ranging over 9 orders of magnitude from 1177 · 106 J day1 m3 to 1177 · 103 Jday1 m3. PdB The ratio of relative rate of increase of biomass over relative production variations ðBdPÞ as well as the size-dependent predatory mortality rate, functional response and growth rate are computed at each production level considered. To consider transitional behavior, oscillations of primary production P are simulated at three different reference production levels (1177 · 106 Jday1 m3, 117.7 J day1 m3 and 1177 · 103 Jday1 m3). During one oscillation period, primary production varies from 0.5 to 2 times the reference value. Two time-periods are considered: 365 days (one year) and 1825 days (5 years). The effect of a sudden temporary change in primary production P is compared to the effect of a permanent change (regime shift) in both cases of an increase and a decrease of primary production. In a second set of simulations, the effect of temperature variations is explored. The stationary size-spectrum and its associated total biomass are computed for seven temperature values ranging from 5 Cto29C with a reference temperature fixed at 298.5 K (25 C) which is a typical average temperature in tropical waters. Tem- perature oscillations are simulated with a 10 C amplitude. As for primary production, two time-periods are considered: 365 days (1 year) and 1825 days (5 years).

3. Environmental eﬀects on the size-spectrum

3.1. Bottom-up eﬀects of primary production variability

The first set of numerical experiments explores the effect of changes in the production of phytoplankton P. When the phytoplanktonic production is increased above the reference value, the stationary size-spectrum is translated upward (Fig. 4): the intercept increases but the slope does not change. For very high values of phytoplankton production, the biomass of very small organisms (first size classes) decreases without affecting the medium and large size classes. The energy in small size classes is maintained at low values but the flux of energy through those classes remains high enough to maintain the size spectrum. If the phytoplankton production is decreased below the reference value, the stationary size-spectrum is only slightly translated downward (the intercept decreases very slowly and the slope does not change) but L1 decreases markedly. For very low phytoplankton production, the ecosystem collapses. The nonlinearity of the size-spectrum response to changes in phytoplankton production appears clearly when considering the total biomass of the ecosystem and the biomass per unit of phytoplankton production as a function of phytoplankton production (Fig. 5a and b). Three domains can be delimited. The first one, which corresponds to low production levels, is characterized by the independence of total biomass and phytoplankton production and by high biomass per unit of production. The second one, which corresponds to medium production levels, is characterized by the appearance of a relationship between total biomass and phytoplankton production and by medium biomass per unit of production. The third domain, which corresponds to high production levels, is characterized by the proportionality of total biomass to phytoplankton production and by low biomass per unit of production. Any increase of phytoplankton production does not change the ecosystem biomass at low phytoplankton production, causes increasing changes in the ecosystem biomass at medium phytoplankton production and causes proportional changes in the ecosystem biomass at high primary production (Fig. 5c). At very low primary production levels, the log–log predatory mortality curve shows a linearly decreasing trend for organisms between 2 mm and 10 cm (Fig. 5d) with higher mortality rates for producers. For larger organisms, the predation mortality decreases sharply down to zero for length above 70 cm. The curve does not change much when primary production increases at low production levels. At low to medium primary production levels, predation mortality increases sharply for large sizes between 10 cm and 1 m. From medium to high production levels, predatory mortality increases for all size classes except for large animals for which it does O. Maury et al. / Progress in Oceanography 74 (2007) 500–514 505

Prod=1177.103 J.day-1 .m-3 Prod=1177.102 J.day-1 .m-3

Prod=1177.101 J.day-1 .m-3 Prod=1177 J.day-1 .m-3 1.E+11 Prod=1177.10-1 J.day-1 .m-3 Prod=1177.10-2 J.day-1 .m-3 1.E+10 Prod=1177.10-3 J.day-1 .m-3 Prod=1177.10-4 J.day-1 .m-3 1.E+09 Prod=1177.10-5 J.day-1 .m-3 Prod=1177.10-6 J.day-1 .m-3 1.E+08

) 1.E+07 -3

.m 1.E+06 -1 1.E+05 1.E+04 1.E+03 1.E+02 1.E+01

Energy density (J.kg density Energy 1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 0.001 0.01 0.1 1 10 Organisms length (m)

Fig. 4. Steady state size-spectrum obtained for primary production levels increasing from 1177 · 106 J day1 m3 to 1177 · 103 J day1 m3.

not change much. The predatory mortality curve crosses the nonpredatory mortality curve at a critical size equal to 8 cm at low production levels which increases up to 35 cm at high production levels. This critical size separates two domains where either predatory mortality is predominant (small sizes) or nonpredatory mortality is dominant (large sizes). At high production levels the predatory mortality undergone by small organisms (<1 cm) reaches quite high levels. The functional response increases with organism size from the highly food-limited small sizes to the less limited large sizes. When primary production increases, the functional response increases, reaching 1 (no limitation) for large animals first then for smaller sizes (Fig. 5e). The growth rate (in weight) as a function of organism size is dome-shaped, reaching a maximum for intermediate to large sizes and then decreasing down to zero for length equal to L1 (Fig. 5f). Both L1 and the maximum growth rate decrease when phytoplankton production decreases. Oscillations of phytoplankton production have been simulated for three mean production levels corresponding to the three domains identified. At medium and high mean production levels, oscillations appear and propagate along the size-spectrum (Fig. 6a and b). The relative amplitude of the propagating waves is maximal and exceeds largely the relative amplitude of primary production in a ‘‘resonant domain’’ approximately comprised between 3 and 90 cm for yearly phytoplankton oscillations (Fig. 6a and c) and between 20 cm and 2 m for 5 year period phytoplankton oscillations (Fig. 6b and d). The phase of the oscillations in the ‘‘resonant range’’ varies with size but their frequency keeps approximately constant, equating the frequency of primary production oscillations. At low mean production levels, the spectrum remains stable for yearly phytoplankton oscillations and its intercept varies without appearance of a ‘‘resonance domain’’ when phytoplankton oscillates at a 5 year period. A sudden and temporary (one month) increase (bloom) or decrease (drop) of the primary production leads to important biomass variations before the systems returns to its steady state level (Fig. 7a and b). If the bloom is strong enough (primary production ·10), the perturbation amplifies in the trophic chain and biomass exhibits two peaks with very high levels almost one year and half after the bloom (Fig. 7a). When the drop is very strong (primary production/10), the biomass also shows important oscillations but on a much shorter three months time period (Fig. 7b). Conversely, a permanent change in primary production (shift) of the same 506 O. Maury et al. / Progress in Oceanography 74 (2007) 500–514

ab1.E+07 1.00E+07 1.E+06 Dissipation 1.E+05 1.00E+06 1.E+04 Loss 1.E+03 Transition 1.00E+05

) 1.E+02 Loss -3 1.E+01 1.00E+04 1.E+00 1.E-01 1.00E+03 1.E-02

Energy (J.m 1.E-03 Eggs energy Transition 1.E-04 1.00E+02 Total energy 1.E-05 Production Dissipation 1.00E+01 1.E-06 (biomass/production) turnover 1.E-07 1.E-08 1.00E+00 1.E-08 1.E-06 1.E-04 1.E-02 1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.00E-08 1.00E-06 1.00E-04 1.00E-02 1.00E+00 1.00E+02 1.00E+04 1.00E+061.00E+0 8

-1 -3 Primary prodution (J.day-1.m-3) Primary production (J.day .m )

c 1.2E+00 d 1.E+02 Dissipation

1.0E+00 1.E+00 ) -1 8.0E-01 1.E-02

Transition 1.E-04 6.0E-01

1.E-06 4.0E-01 (P.d(B))/(B.d(P))

3 -1 -3 2 -1 -3 1.E-08 Prod=1177.10 J.day .m Prod=1177.10 J.day .m 1 -1 -3 -1 -3 2.0E-01 Loss Predatory mortality (day Prod=1177.10 J.day .m Prod=1177 J.day .m Prod=1177.10-1 J.day-1.m-3 Prod=1177.10-2 J.day-1.m-3 -3 -1 -3 -4 -1 -3

Relative rateof increase ofbiomass 1.E-10 Prod=1177.10 J.day .m Prod=1177.10 J.day .m 0.0E+00 Prod=1177.10-5 J.day-1.m-3 Prod=1177.10-6 J.day-1.m-3 1.E-08 1.E-06 1.E-04 1.E-02 1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 M 1.E-12 0.001 0.01 0.1 1 10 -1 -3 Primary production (J.day .m ) Organisms length (m)

e f 0.045 Prod=1177.103 J.day-1.m-3 1 Prod=1177.102 J.day-1.m-3 0.04 Prod=1177.101 J.day-3 .m-3 Prod=1177 J.day-1.m-3 0.035 -1 -1 -3 0.8 Prod=1177.10 J.day .m ) -2 -1 -3

-1 Prod=1177.10 J.day .m 0.03 Prod=1177.10-3 J.day-1 .m-3 Prod=1177.10-4 J.day-1 .m-3 0.6 0.025 Prod=1177.10-5 J.day-1 .m-3 Prod=1177.10-6 J.day-1 .m-3 0.02 0.4

Functional response Functional -1 -3 0.015 Prod=1177.103 J.day-1 .m-3 Prod=1177.102 J.day .m Prod=1177.101 J.day-1 .m-3 Prod=1177 J.day-1 .m-3 Growth rate (kg.day 0.01 0.2 Prod=1177.10-1 J.day-1 .m-3 Prod=1177.10-2 J.day-1 .m-3 -3 -1 -3 -4 -1 -3 Prod=1177.10 J.day .m Prod=1177.10 J.day .m 0.005 -1 -3 Prod=1177.10-5 J.day .m Prod=1177.10-6 J.day-1 .m-3 0 0 0 0.2 0.4 0.6 0.81 1.2 1.4 1.6 1.8 2 0 0.2 0.4 0.6 0.81 1.2 1.4 1.6 1.8 2 Organisms length (m) Organisms length (m)

Fig. 5. (a) steady state biomass of the ecosystem versus primary production, (b) biomass/primary production ratio versus primary PdB production, (c) relative rate of increase of biomass when production increases ðBdPÞ versus primary production, (d) nonpredatory mortality M and steady state predatory mortality versus body size for primary production levels increasing from 1177 · 106 J day1 m3 to 1177 · 103 J day1 m3, (e) steady state functional response versus body size for primary production levels increasing from 1177 · 106 J day1 m30 to 1177 · 103 J day1 m3, (f) steady state growth rate versus body size for primary production levels increasing from 1177 · 106 J day1 m3 to 1177 · 103 J day1 m3. magnitude does not result in unstable behavior of the model: biomass quickly evolves toward its new steady state level after small oscillations (Fig. 7a and b).

3.2. Eﬀects of temperature

When temperature increases from 5 Cto29C, the steady state size-spectrum is translated downward (same slope and decreasing intercept) (Fig. 8a) and the total ecosystem biomass at steady state decreases sharply, with a rate of decrease depending on the primary production level (Fig. 8b). At low primary production level, ecosystem biomass is almost proportional to the inverse of the Arrhenius coeﬃcient (Fig. 8b). When temperature increases, the functional response decreases (Fig. 8c and d), and both the growth rate and the predatory mortality rate increase markedly (Fig. 8e and f). When temperature oscillates, waves propagate along the spectrum (Fig. 8g and h) with a ‘‘resonant domain’’ approximately comprised between 3 and 90 cm for yearly oscillations (Fig. 8i) and between 20 cm O. Maury et al. / Progress in Oceanography 74 (2007) 500–514 507

1.E+15 1.E+15 ab1.E+14 1.E+14 1.E+13 1.E+13 1.E+12 1.E+12 1.E+11 1.E+11 ) ) -3

-3 1.E+10 1.E+10 .m .m 1.E+09 1.E+09 -1 -1 1.E+08 1.E+08 1.E+07 1.E+07 1.E+06 1.E+06 1.E+05 1.E+05 1.E+04 1.E+04 1.E+03 1.E+03 1.E+02 1.E+02 1.E+01 1.E+01 Energy density (J.kg density Energy 1.E+00 (J.kg density Energy 1.E+00 1.E-01 1.E-01 1.E-02 1.E-02 1.E-03 1.E-03 1.E-04 1.E-04 0.001 0.01 0.1 1 10 0.001 0.01 0.1 1 10 Organisms length (m) Organisms length (m)

cd4 4

3.5 3.5

3 3

2.5 2.5

2 2

1.5 1.5

Relative energydensity 1 Relative energydensity 1

0.5 0.5

0 0 0.001 0.01 0.1 1 10 0.001 0.01 0.1 1 10 Organisms length (m) Organisms length (m)

Fig. 6. Effect of primary production oscillations on the size-spectrum at three mean production levels (1177 · 106 J day1 m3, 117.7 J day1 m3 and 1177 · 103 J day1 m3) in the case of yearly oscillations (a) and 5 years period oscillations (b). (c) and (d) are the same figures drawn in value relative to the mean. For figures (a) and (c), continuous lines represent the monthly spectrum, circles correspond to the first month and triangles to the 6th month. For figures (b) and (d), continuous lines represent the spectrum every 5 months, circles correspond to the first month and triangles to the 30th month.

3 ab30

2.5 shift x5 shift /5 25 bloom x5 drop /5 shift x10 2 shift /10 20 bloom x10 drop /10 biomass

biomass 1.5 15

1 10 steady state Biomass relative tothe steady state Biomass relative to the

5 0.5

0 0 13640 13820 14000 14180 14360 14540 14720 14900 13640 13820 14000 14180 14360 14540 14720 14900 Time (days) Time (days)

Fig. 7. Eﬀect of a sudden and temporary primary production increase (bloom) or a sudden and permanent increase (shift) on ecosystem biomass (a). Eﬀect of a sudden and temporary primary production decrease (drop) or a sudden and permanent decrease (shift) on ecosystem biomass (b). and 2 m for 5 years period temperature oscillations (Fig. 8j). The phase of the oscillations in the ‘‘resonant range’’ varies with size but their frequency keeps approximately constant, equating the period of the oscillations of temperature. 508 O. Maury et al. / Progress in Oceanography 74 (2007) 500–514

4. Discussion

4.1. Eﬀects of variations of primary production

The relationship between primary production and the total biomass of the ecosystem is of considerable theoretical and practical interest and has been the subject of various studies. It is generally concluded, both the-

ab1.E+12 8 1.E+11 1.E+10 7 1/Arhenius coefficient 5°C Prod=1177.104 J.day-1.m-3 ) 1.E+09 9°C 3 -3 -3 Prod=1177.10 J.day-1.m 13°C 2 -3 .m 1.E+08 6 Prod=1177.10 J.day-1.m -1 17°C Prod=1177.101 J.day-1.m-3 -1 -3 1.E+07 21°C Prod=1177 J.day .m 5 Prod=1177.10-1 J.day-1.m-3 1.E+06 25°C Prod=1177.10-2 J.day-1.m-3 1.E+05 29°C -3 -3 4 Prod=1177.10 J.day-1.m Prod=1177.10-4 J.day-1.m-3 1.E+04 1.E+03 3 1.E+02 Energy density (J.kg density Energy 1.E+01 2 Inverse Arrhenius coefficient

1.E+00 Relative ecosystem biomass (RB) 1 1.E-01 0.001 0.01 0.1 1 10 0 Organisms length (m) 510152025 Temperature (°C)

cd1 1 0.9 0.9

0.8 0.8

0.7 0.7 5°C 5°C 9°C 0.6 0.6 9°C 13°C 13°C response 0.5 17°C 0.5 17°C 21°C 21°C 0.4 25°C 0.4 25°C

Functional response 29°C 29°C 0.3 0.3 Functional Functional

0.2 0.2

0.1 0.1

0 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.001 0.01 0.1 1 10 Organisms length (m) Organisms length (m)

0.06 10 ef5°C 9°C 1 0.05 13°C 0.001 0.01 0.1 1 10 17°C 0.1

) 21°C -1 )

-1 0.01 0.04 25°C 5°C 29°C 0.001 9°C 13°C 0.03 0.0001 17°C 21°C 0.00001 0.02 25°C 29°C Growth rate (kg.day 0.000001

0.01

Predatory mortality (day 0.0000001

0.00000001 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.000000001 Organisms length (m) Organisms length (m)

Fig. 8. (a) effect of increasing the temperature from 5 Cto29C on the stationary size-spectrum at medium production level (1177 J day1 m3); (b) effects of temperature on relative ecosystem biomass (biomass at T/biomass at 25 C) at different production levels (from low 1177 · 104 J day1 m3 to high 1177 · 104 J day1 m3); (c) effects of temperature on the size-specific functional response, (d) same figure with a log scale abscissa (e) temperature effects on the size-dependent growth rate (f) temperature effect on the size-dependent predatory mortality coefficient (g) effects of temperature yearly oscillations on the size-spectrum; (h) the same with five years period oscillations; (i) same than (g) expressed in relative values; (j) same than (h) expressed in relative values. O. Maury et al. / Progress in Oceanography 74 (2007) 500–514 509

gh1.E+12 1.E+12 1.E+11 1.E+11 1.E+10 1.E+10 ) ) -3

1.E+09 -3 1.E+09 .m .m -1

1.E+08 -1 1.E+08 1.E+07 1.E+07 1.E+06 1.E+06 1.E+05 1.E+05 1.E+04 1.E+04 1.E+03 1.E+03 Energy density (J.kg density Energy 1.E+02 (J.kg density Energy 1.E+02 1.E+01 1.E+01 1.E+00 1.E+00 1.E-01 1.E-01 0.001 0.01 0.1 1 10 0.001 0.01 0.1 1 10 Organisms length (m) Organisms length (m)

ij2.5 2.5

2 2

1.5 1.5

1 1 Relative energy density Relative energy density 0.5 0.5

0 0 0.001 0.01 0.1 1 10 0.001 0.01 0.1 1 10 Organisms length (m) Organisms length (m)

Fig. 8 (continued ) oretically and empirically, that the intercept of the size-spectrum and hence the total biomass of the ecosystem are proportionally related to primary production (Shin and Cury, 2004; Benoit and Rochet, 2004; Ware and Thomson, 2005). Our ﬁndings extend this result and show that this apparent proportionality between the total biomass in the ecosystem and the phytoplankton production may only occur locally, at high and stable primary production levels (Figs. 4 and 5a). At low phytoplankton production levels, the simulated ecosystem biomass appears indeed to be independent of phytoplankton production (Fig. 5a). In this domain, any increase of the primary production is lost (Fig. 5c). The nonlinear response of ecosystem biomass to phytoplankton production is related to the use of a nonlinear functional response which decreases the ability of predators to eat prey at low prey density. Indeed, when phytoplankton production is low, ecosystem biomass is globally low, leading to low functional response of the predatory organisms which are food-limited (Fig. 5e) and have therefore low growth and reproduction rates and small L1 (Fig. 5f). In this low production domain, predation, growth and reproduction are slow processes compared to nonpredatory mortality (Fig. 5d) so that organisms die for other causes than predation faster than they grow and reproduce: the ecosystem loses energy. We call this domain the ‘‘loss domain’’ because losses (nonpredatory mortality) are dominant over dissipation (biological work). Conversely, when phytoplankton production is high, ecosystem biomass is globally high, leading to saturated functional response of predators which are satiated (except for the very small organisms) (Fig. 5e). It follows that predation, growth and reproduction rates as well as L1 are maximal (Fig. 5f). In this production domain, predation, growth and reproduction are fast processes compared to nonpredatory mortality (Fig. 5d) so that organisms grow and reproduce faster than they die: the ecosystem accumulates energy and dissipates it through metabolic work. We call this domain the ‘‘dissipation domain’’ because dissipation due to biological work is dominant over losses. 510 O. Maury et al. / Progress in Oceanography 74 (2007) 500–514

In an apparent paradox, the loss domain (low production) corresponds to very high ecosystem biomass/ primary production ratios (Fig. 5b). It means that at low production levels, when the ecosystem is not very efficient in transferring energy from small sizes to large sizes and dissipating it, biomass remains stable at a minimal value for a wide range of production levels, leading potentially to very high B/P ratios (however, very low levels of primary production lead to a biomass decrease below its minimal level and induce the collapse of the ecosystem). Johnson (1983, 1994a,b) and Vanriel and Johnson (1995) describe the ecology of closed ecosystems such as arctic lakes where very low primary production levels sustain high fish biomass composed by very old individuals. Generalizing their observations, they hypothesize that ecosystem dynamics are driven by two countervailing attractors: one of ‘‘zero dissipation’’ or complete stability (state of ‘‘most action’’) which tends to decelerate energy flow through ecosystems and one of maximal dissipation (state of ‘‘least action’’, Feynman, 1963) which tends to accelerate energy flow through ecosystems and where organisms, as any physical systems, dissipate energy. Finally, they conclude that ‘‘forces within organisms and ecosystems must override the principle of least action and move toward a state of most action’’ which could be the major characteristic of living systems. Our simulations suggest that, as observed by Johnson (1983, 1994a,b), very low primary production levels lead to high biomass/primary production ratios (Fig. 5b) and exhibit low predatory mortality and hence old individuals. They furthermore show that the state of maximal dissipation (least action) is only reached at high primary production levels when the ecosystem is efficient in transferring energy from small sizes to large sizes. Conversely, a state of least dissipation (most action) characterizes the simulated ecosystem at low primary production levels when it is not efficient in dissipating energy. The different responses of biomass to production that we observe have however to be put into perspective since in real ecosystems, an important fraction of the dead organisms is consumed by decomposers (mostly bacteria) which are prey at the basis of the food web. Consequently, a large part of the energy which is lost by death is actually re-injected into the system (Valiela, 1995). This feedback phenomenon, which is non-neg- ligible in low production systems (Parson and Lalli, 2000), could change the relationship that we obtain at low production levels. Conversely, in very high production systems, problems of anoxia are known to become predominant and may lead to massive death of organisms, changing the relationship that we obtain at high production levels. It is interesting to note that at very high and stable production levels, the ecosystem is so efficient that the small organisms are literally swept out from the water by predation and growth: they are eaten and grow as soon as they are produced, leading to a size-spectrum curved downward for small sizes (Fig. 4). Such hyper- depletion phenomenon for small sizes has been observed by several authors (e.g., Pope and Knights, 1982; Bianchi et al., 2000) in various ecosystems worldwide; it leads to curved size-spectra for small body sizes. When oscillations of primary production are simulated, the model predicts that waves propagate along the spectrum (Fig. 6a and b) and amplify until they reach a maximum amplitude in a given weight range before decreasing for larger size classes (Fig. 6c and d). The size range corresponding to the maximum amplitude of the relative energy density, that we call the ‘‘resonant range’’, depends on the period of the primary production oscillations (Fig. 6c and d). High frequency production oscillations lead to a ‘‘resonant range’’ occurring for small sizes when low frequency oscillations lead to a ‘‘resonant range’’ occurring for large sizes. Small organisms feed on producers or on very close size ranges. They furthermore grow and die very quickly (their characteristic time – the time needed to reach a given size – is much shorter than the phytoplankton oscillations period – 1 year) so that they can adapt very rapidly to changes and track primary production variability. In consequence, they oscillate more or less in phase with producers (Fig. 6c and d): they are bottom-up controlled by primary production oscillations. When body size increases, the characteristic time also increases. When the characteristic time approaches the period of phytoplankton oscillations, the system enters the ‘‘resonant range’’: prey and predators begin to oscillate out of phase with alternative periods of top-down and bottom-up control. Oscillations amplify with size until a maximum level which is reached when the entire preyed size range oscillates synchronously, out of phase with their smallest predator. Finally, organisms larger than the ‘‘resonant range’’ feed on a wide range of prey size covering several out of phase oscillations. They are emancipated from the temporary disappearance of a certain size range of their prey since they can compensate by reporting their predation effort on abundant size classes: they are not influenced by bottom-up effects of phytoplankton high frequency oscillations. O. Maury et al. / Progress in Oceanography 74 (2007) 500–514 511

Oscillations of the size spectrum have been reported by various authors (Jime´nez et al., 1989; Edvardsen et al., 2002; Fossheim et al., 2005). For instance, Fossheim et al. (2005, Fig. 5)) observed oscillations for small sizes (up to 1 mm) of zooplankton size spectrum recorded with an Optical Plankton Counter (OPC). Given their frequency and the very fast growth rate of zooplankton, those oscillations could be linked to nyctimeral oscillations of the zooplankton feeding activity.

4.2. Eﬀects of temperature

Temperature plays a major role in most chemical reactions and biochemical processes. Consequently, it controls all physiological rates including growth, respiration, reproduction, movements, ageing, etc. (Kooij- man, 2000; Gillooly et al., 2001, 2002; Clarke, 2004; Clarke and Fraser, 2004; Speakman, 2005). As most marine fishes are poı¨kilotherms, water temperature has a direct influence on all aspects of their metabolism (Clarke and Johnston, 1999). As a result, the speed and efficiency of energy transfer through the food chain should also be strongly influenced by temperature (Enquist et al., 2003). However, despite an obvious statistical effect of temperature on physiological rates at the inter-specific level, mechanistic rules are lacking to rig- orously explain the effects of temperature at the ecosystem scale, where purely chemical effects are altered by complex eco-evolutionary processes (Clarke, 2004; Clarke and Fraser, 2004). Furthermore, due to the diffi- culty of designing appropriate experiments on real ecosystems, empirical studies dealing with the global effects of temperature on marine ecosystems are lacking. In this context, our results provide testable insights about the potential effects of temperature on marine ecosystems. Our simulations show that when temperature increases at constant primary production, the slope of the stationary size-spectrum does not change but its intercept decreases markedly (Fig. 8a). It means that at constant primary production, temperature does not influence the steady state size structure of the ecosystem (the biomass of a size-class relatively to one another) but it modifies the total amount of biomass in the ecosystem at steady state (Fig. 8b). When temperature oscillates, the model predicts that waves propagate along the spectrum (Fig. 8g and h) and amplify until a ‘‘resonant range’’ which depends on the period of temperature oscillations (Fig. 8i and j). The oscillating size-spectra resemble those obtained with primary production oscillations but are however more complex, with the appearance of a double ‘‘resonant range’’ (Fig. 8i and j). In real ecosystems, those oscillations are likely to superimpose with the oscillations caused by fluctuations of primary production. In our model, total biomass depends only on primary production, which is assumed to be independent of temperature, and loss and dissipation rates which are dependent on temperature. If we consider the dBðT Þ system at steady state dt ¼ 0 , production equals losses + dissipation. If we furthermore assume that the system is in the loss domain (low primary production), nonpredatory mortality (losses) prevails over dissipation processes (biological work). As a result, the dissipation terms (see the full model equation in Maury et al. (2007) Appendix A) which are nonlinear with respect to the Arrhenius correction factor A(T) can be neglected against losses which are proportional to A(T). It follows that in the loss domain the total steady state biomass can be approximated to be inversely proportional to the Arrhenius temper- production ature-dependent correction factor ðproduction ¼ AðT Þloss rates BðT Þ()BðT Þ¼AðT Þloss ratesÞ and hence that total biomass relative to total biomass at the reference temperature varies as the inverse of the Arrhe- nius coefficient: BðT Þ 1 ¼ ð2Þ BðT ref Þ AðT Þ This approximation works well in the loss domain (Fig. 8b). It is still acceptable in the transition domain but it does not hold anymore in the dissipation domain (Fig. 8b) when nonlinear dissipation processes dominate over linear loss process. This result is particularly important in a global warming context. It suggests that at constant primary production, the impact of changes of water temperature on ecosystem biomass will be heterogeneous and will vary with the absolute level of primary production. In our simulations (with a reference temperature Tref =25C), a 2–4 C increase of water temperature leads to 20–43% decrease of the total ecosystem biomass in oligotrophic regions and to 15–32% decrease of biomass in eutrophic regions (Fig. 9). 512 O. Maury et al. / Progress in Oceanography 74 (2007) 500–514

-50%

-45% Loss domain -40% Dissipation domain

-35%

-30%

-25%

-20%

-15%

Change in biomass (%) -10%

-5%

0% Tref+ 2°C Tref + 4°C Change in the reference temperature

Fig. 9. predicted changes of ecosystem biomass due to a 2 Cto4C warming of seawater in the loss domain (oligotrophic) and in the dissipation domain (eutrophic).

Those results have however to be put into perspective since in our model, primary production is assumed to be independent from temperature. The response of phytoplankton photosynthetic activity to temperature is yet clear at a species level. However, ‘‘there are few observations that demonstrate important eﬀects of temperature on rates of primary production in the sea’’ (Valiela, 1995). Furthermore, phytoplankton production is highly dependent on a variety of hydrological processes (e.g. Valiela, 1995; Mann and Lazier, 1996) which are in turn linked to temperature in a variety of ways. To avoid unnecessary complexity, we decided to neglect the inﬂuence of temperature on primary production. Nevertheless, recent studies (e.g. Richardson and Scho- eman, 2004) show that phytoplankton abundance could be positively correlated with temperature in cooler regions and negatively correlated to temperature in warmer regions. If those correlations hold, any increase of seawater temperature in cooler regions (generally enriched, so likely to be in the dissipation domain) would lead to an increase of phytoplankton which could compensate for the decrease of ecosystem biomass that we predict. Conversely, in warm areas (which are generally oligotrophic, so likely to be in the loss domain), seawater warming would decrease primary production and hence would amplify the decrease of ecosystem biomass that we predict when temperature increases.

5. Conclusion

The way solar energy is transferred and dissipated along food chains, from phytoplankton up to top predators is central to ecology (Lindeman, 1942). Understanding energy fluxes through ecosystems implies an understanding of the complex relationships linking primary production to the biomass of the ecosystem it sus- tains. These relationships are of considerable theoretical interest and have important practical implications for fisheries management. In this paper we focused on the impact of primary production and temperature on the size spectrum of marine ecosystems. Using numerical simulations with an ecosystem model, we established that both primary production and temperature could have synergistic nonlinear effects on the intercept of the size spectrum and thus on the total ecosystem biomass. Our results suggest that global environmental changes will have important but heterogeneous effects on marine ecosystem biomass. They furthermore suggest that environmental variability causes waves that propagate along the size spectrum, until a resonant range where the relative amplitude of fluctuations is maximal. This resonant range depends on the frequency of the environmental forcing: high frequency variability of the environment leads to important biomass variability for small organisms whereas low frequency variability leads to important biomass variability for large organisms. This implies frequency-dependent time lags between environmental changes and the associated ecosystem responses. The variability of real environments is characterized by a multiplicity of frequencies which should lead to multiple superimposed waves reasoning on a variety of size ranges. Real ecosystems are furthermore characterized by an important spatial heterogeneity and by transport and movements of organisms. Associated to the lag effects, those processes probably lead to very complex convoluted dynamics of energy flux through the size spectrum. Understanding the way real ecosystems respond to environmental variability and predicting their evolution with climate change will require those phenomena to be addressed explicitly, using spatially explicit size-based ecosystem models. O. Maury et al. / Progress in Oceanography 74 (2007) 500–514 513

Acknowledgements

We thank Bernard Cazelles, Philippe Cury, Alain Menesguen, Fre´de´ric Me´nard and Christian Mullon for their constructive criticisms of an earlier version of the manuscript and for their kind encouragements.

References

Benoit, E., Rochet, M.J., 2004. A continuous model of biomass size spectra governed by predation and the effects of fishing on them. Journal of Theoretical Biology 226, 9–21. Bianchi, G., Gislason, H., Graham, K., Hill, L., Jin, X., Koranteng, K., Manickchand-Heileman, S., Paya, I., Sainsbury, K., Sanchez, F., Zwanenburg, K., 2000. Impact of fishing on size composition and diversity of demersal fish communities. ICES Journal of Marine Science 57, 558–571. Blueweiss, L., Fox, H., Kudzma, V., Nakashima, D., Peters, R., Sams, S., 1978. Relationships between body size and some life history parameters. Oecologia 37, 257–272. Boudreau, P.R., Dickie, L.M., 1992. Biomass spectra of aquatic ecosystems in relation to fisheries yield. Canadian Journal of Fishery and Aquatic Science 49, 1528–1538. Brown, J.H., Gillooly, J.F., 2003. Ecological food webs: high-quality data facilitate theoretical unification. Proceedings of the National Academy of Sciences (USA) 100, 1467–1468. Clarke, A., Fraser, K.P.P., 2004. Why does metabolism scale with temperature? Functional Ecology 18, 243–251. Clarke, A., 2004. Is there a Universal Temperature Dependence of metabolism? Functional Ecology 18, 252–256. Clarke, A., Johnston, N.M., 1999. Scaling of metabolic rate with body mass and temperature in teleost fish. Journal of Animal Ecology 68, 893–905. Cousins, S.H., 1980. A trophic continuum derived from plant structure, animal size and a detritus cascade. Journal of Theoretical Biology 82, 607–618. Cury, P., Shannon, L., Shin, Y.-J., 2003. The functioning of marine ecosystems: a fisheries perspective. In: Sinclair, M., Valdimarsson, G. (Eds.), Responsible Fisheries in the Marine Ecosystem. FAO, Cabi, p. 426p. Edvardsen, A., Zhou, M., Tande, K.S., Zhu, Y., 2002. Zooplankton population dynamics: measuring in situ growth and mortality rates using an optical plankton counter. Marine Ecology Progress Serie 227, 205–219. Enquist, B.J., Economo, E.P., Huxman, T.E., Allen, A.P., Ignace, D.D., Gillooly, J.F., 2003. Scaling metabolism from organisms to ecosystems. Nature 423, 639–642. Feynman, R.P., 1963. The principle of least action. In: Feynman, R.P., Leighton, R.B., Sands, M. (Eds.). The Feynman Lectures on Physics, vol. 2. Addison-Wesley, Reading, Massachusetts, USA. Fossheim, M., Zhou, M., Tande, K.S., Pedersen, O.-P., Zhu, Y., Edvardsen, A., 2005. Interactions between biological and environmental structures along the coast of northern Norway. Marine Ecology Progress Serie 300, 147–158. Gillooly, J.F., Brown, J.H., West, G.B., Savage, V.M., Charnov, E.L., 2001. Effects of size and temperature on metabolic rate. Science 293, 2248–2251. Gillooly, J.F., Charnov, E.L., West, G.B., Savage, V.M., Brown, J.H., 2002. Effects of size and temperature on developmental time. Nature 417, 70–73. Jennings, S., Pinnegar, J.K., Polunin, N.V.C., Boon, T., 2001. Weak cross-species relationships between body size and trophic level belie powerful size-based trophic structuring in fish communities. Journal of Animal Ecology 70, 934–944. Jennings, S., Pinnegar, J.K., Polunin, N.V.C., Warr, K.J., 2002. Linking size-based and trophic analyses of benthic community structure. Marine Ecology Progress Serie 226, 77–85. Jennings, S., 2005. Size-based analyses of aquatic food webs. In: Belgrano, A., Scharler, U.M., Dunne, J., Ulanowicz, R.E. (Eds.), Aquatic Food Webs, an Ecosystem Approach. Oxford University Press, pp. 86–97. Jimeńez, F., Rodrı´guez, J., Jimenez-Gomez, F., Bautista, B., 1989. Bottlenecks in the propagation of a fluctuation up the planktonic size spectrum in Mediterranean coastal waters. In: Ros, J.D. (Ed.), Topics in Marine Biology. Scientia Marina 53 (2–3), 269–275. Johnson, L., 1983. Homeostatic Characteristics of Single Species Fish Stocks in Artic Lakes. Canadian Journal of Fishery and Aquatic Science 40, 987–1024. Johnson, L., 1994a. Long-term experiments on the stability of two fish populations in previously unexploited Arctic Lakes. Canadian Journal of Fishery and Aquatic Science 51, 209–225. Johnson, L., 1994b. Pattern and processes in ecological systems: a step in the direction of a general ecological theory. Canadian Journal of Fishery and Aquatic Science 51, 226–246. Kerr, S.R., Dickie, L.M., 2001. The Biomass Spectrum: A Predator–Prey Theory of Aquatic Production. Columbia University Press, New York, 320p. Kooijman, S.A.L.M., 1986. Energy budgets can explain body size relations. Journal of Theoretical Biology 121, 269–282. Kooijman, S.A.L.M., 2000. Dynamic Energy and Mass Budgets in Biological Systems. Cambridge University Press, Cambridge, 424p. Kooijman, S.A.L.M., 2001. Quantitative aspects of metabolic organization: a discussion of concepts. Philosophical Transactions of the Royal Society of London, B. 356, 331–349. Lindeman, R.L., 1942. The trophic-dynamic aspect of ecology. Ecology 23, 399–418. Lundvall, D., Svanba¨ck, R., Persson, L., Bystro¨m, P., 1999. Size dependent predation in piscivores: interactions between predator foraging and prey avoidance abilities. Canadian Journal of Fishery and Aquatic Science 56, 1285–1292. 514 O. Maury et al. / Progress in Oceanography 74 (2007) 500–514

Mann, K.H., Lazier, J.R.N., 1996. Dynamics of Marine Systems. Blackwell science, 394p. Marquet, P.A., Quinõnes, R.A., Abades, S., Labra, F., Tognelli, M., Arim, M., Rivadeneira, M., 2005. Scaling and power-laws in ecological systems. The Journal of Experimental Biology 208, 1749–1769. Maury, O., Faugeras, B., Shin, Y.-J., Poggiale, J.-C., Ben Ari, T., Marsac, F., 2007. Modeling environmental effects on the size-structured energy flow through marine ecosystems. Part 1: the model. Progess in Oceanography 74 (4), 479–499. Nisbet, R.M., Muller, E.B., Lika, K., Kooijman, S.A.L.M., 2000. From molecules to ecosystems through dynamic energy budget models. Journal of Animal Ecology 69, 913–926. Parson, T.R., Lalli, C.M., 2000. Jellyfish population explosions: revisiting a hypothesis of possible causes. La mer, 11–121. Pope, J.G., Knights, B.J., 1982. Comparison of length distributions of combined catches of all demersal fishes in surveys in the North Sea and at Faroe Bank. In: Mercer, M.C. (Ed.), Multispecies Approaches to Fisheries Management. Advice. Canadian Special Publication in Fisheries and Aquatic Sciences 59, 116–118. Richardson, A.J., Schoeman, D.S., 2004. Climate impact on plankton ecosystems in the Northeast Atlantic. Science 305, 1609–1612. Scharf, F.S., Juanes, F., Rountree, R.A., 2000. Predator size-prey size relationships of marine fish predators: interspecific variation and effects of ontogeny and body size on trophic-niche breadth. Marine Ecology Progress Serie 208, 229–248. Sheldon, R.W., Prakash, A., Sutcliffe, W.H.J., 1972. The size distribution of particles in the ocean. Limnological Oceanography 17 (3), 327–340. Shin, Y.-J., Cury, P., 2004. Using an individual-based model of fish assemblages to study the response of size spectra to changes in fishing. Canadian Journal of Fishery and Aquatic Science 61, 414–431. Shin, Y.-J., Rochet, M.J., Jennings, S., Field, J., Gislason, H., 2005. Using size-based indicators to evaluate the ecosystem effects of fishing. ICES Journal of Marine Science 62, 384–396. Speakman, J.R., 2005. Body size, energy metabolism and lifespan. The Journal of Experimental Biology 208, 1717–1730. Valiela, I., 1995. Marine Ecological Processes. Springer-Verlag, New York, 686p. Vanriel, P., Johnson, L., 1995. Action principles as determinants of ecosystem structure: the autonomous lake as a reference system. Ecology 76 (6), 1741–1757. Ware, D.M., Thomson, R.E., 2005. Bottom-up ecosystem trophic dynamics determine fish production in the Northeast Pacific. Science 308, 1280–1284. West, G.B., Brown, J.H., 2005. The origin of allometric scaling laws in biology from genomes to ecosystems: towards a quantitative unifying theory of biological structure. The Journal of Experimental Biology 208, 1575–1592. Woodward, G., Ebenman, B., Emmerson, M., Montoya, J.M., Olesen, J.M., Valido, A., Warren, P.H., 2005. Body size in ecological networks. Trends in Ecology and Evolution 20 (7), 402–409.